query: who built the world first binary digit computer z1

pos: Z1 (computer) Z1 (computer) The Z1 was a mechanical computer designed by Konrad Zuse from 1935 to 1936 and built by him from 1936 to 1938. It was a binary electrically driven mechanical calculator with limited programmability, reading instructions from punched celluloid film. The Z1 was the first freely programmable computer in the world which used Boolean logic and binary floating-point numbers, however it was unreliable in operation. It was completed in 1938 and financed completely from private funds. This computer was destroyed in the bombardment of Berlin in December 1943, during World War II, together with all construction plans. The Z1

pos: Binary number Mauchly and Norbert Wiener, who wrote about it in his memoirs. The Z1 computer, which was designed and built by Konrad Zuse between 1935 and 1938, used Boolean logic and binary floating point numbers. Any number can be represented by a sequence of bits (binary digits), which in turn may be represented by any mechanism capable of being in two mutually exclusive states. Any of the following rows of symbols can be interpreted as the binary numeric value of 667: The numeric value represented in each case is dependent upon the value assigned to each symbol. In a computer, the

pos: Z1 (computer) poor synchronization due to internal and external stresses on the mechanical parts. The original Z1 was destroyed by the Allied air raids in 1943, but in 1980s Zuse decided to rebuild the machine. First sketches of the Z1 reconstruction were drawn in 1984. He constructed (with the help of two engineering students) thousands of elements of the Z1 again, and finished rebuilding the device in 1989. The rebuilt Z1 (pictured) is displayed at the German Museum of Technology in Berlin. Z1 (computer) The Z1 was a mechanical computer designed by Konrad Zuse from 1935 to 1936 and built by him

pos: Bit January 1947 in which he contracted "binary information digit" to simply "bit". Vannevar Bush had written in 1936 of "bits of information" that could be stored on the punched cards used in the mechanical computers of that time. The first programmable computer, built by Konrad Zuse, used binary notation for numbers. A bit can be stored by a digital device or other physical system that exists in either of two possible distinct states. These may be the two stable states of a flip-flop, two positions of an electrical switch, two distinct voltage or current levels allowed by a circuit, two

pos: Floating-point arithmetic have one more bit of precision. This rule is variously called the "leading bit convention", the "implicit bit convention", the "hidden bit convention", or the "assumed bit convention". The floating-point representation is by far the most common way of representing in computers an approximation to real numbers. However, there are alternatives: In 1914, Leonardo Torres y Quevedo designed an electro-mechanical version of Charles Babbage's Analytical Engine, and included floating-point arithmetic. In 1938, Konrad Zuse of Berlin completed the Z1, the first binary, programmable mechanical computer; it uses a 24-bit binary floating-point number representation with a 7-bit signed exponent, a 17-bit

pos: Z22 (computer) Z22 (computer) The Z22 was the seventh computer model Konrad Zuse developed (the first six being the Z1, Z2, Z3, Z4, Z5 and Z11, respectively). One of the early commercial computers, the Z22's design was finished about 1955. The major version jump from Z11 to Z22 was due to the use of vacuum tubes, as opposed to the electromechanical systems used in earlier models. The first machines built were shipped to Berlin and Aachen. By the end of 1958 the ZMMD-group had built a working ALGOL 58 compiler for the Z22 computer. ZMMD was an abbreviation for Zürich (where Rutishauser

pos: Z3 (computer) demonstrated in 1998 to be, in principle, Turing-complete. However, because it lacked conditional branching, the Z3 only meets this definition by speculatively computing all possible outcomes of a calculation. Thanks to this machine and its predecessors, Konrad Zuse is often regarded as the inventor of the computer. Zuse designed the Z1 in 1935 to 1936 and built it from 1936 to 1938. The Z1 was wholly mechanical and only worked for a few minutes at a time at most. Helmut Schreyer advised Zuse to use a different technology. As a doctoral student at the Berlin Institute of Technology in 1937

pos: Z2 (computer) the successor model Z3. Z2 (computer) The Z2 was a mechanical and relay computer completed by Konrad Zuse in 1940. It was an improvement on the Z1, using the same mechanical memory but replacing the arithmetic and control logic with electrical relay circuits. Photographs and plans for the Z2 were destroyed by the Allied bombing during World War II. In contrast to the Z1, the Z2 used 16-bit fixed-point arithmetic instead of 22-bit floating point. Zuse presented the Z2 in 1940 to members of the DVL (today DLR) and it was especially its member Prof. Alfred Teichmann, whose support achieved

pos: Z2 (computer) Z2 (computer) The Z2 was a mechanical and relay computer completed by Konrad Zuse in 1940. It was an improvement on the Z1, using the same mechanical memory but replacing the arithmetic and control logic with electrical relay circuits. Photographs and plans for the Z2 were destroyed by the Allied bombing during World War II. In contrast to the Z1, the Z2 used 16-bit fixed-point arithmetic instead of 22-bit floating point. Zuse presented the Z2 in 1940 to members of the DVL (today DLR) and it was especially its member Prof. Alfred Teichmann, whose support achieved the partial funding of

pos: Z1 (computer) written to – by the control unit. The mechanical memory units were unique in their design and were patented by Konrad Zuse in 1936. The machine was only capable of executing instructions while reading from the punched tape reader, so the program itself was not loaded in its entirety into internal memory in advance. The input and output were in decimal numbers, with a decimal exponent and the units had special machinery for converting these to and from binary numbers. The input and output instructions would be read or written as floating-point numbers. The program tape was 35 mm film

pos: Logic gate "Tractatus Logico-Philosophicus" (1921). Walther Bothe, inventor of the coincidence circuit, got part of the 1954 Nobel Prize in physics, for the first modern electronic AND gate in 1924. Konrad Zuse designed and built electromechanical logic gates for his computer Z1 (from 1935–38). From 1934 to 1936, NEC engineer Akira Nakashima introduced switching circuit theory in a series of papers showing that two-valued Boolean algebra, which he discovered independently, can describe the operation of switching circuits. His work was later cited by Claude E. Shannon, who elaborated on the use of Boolean algebra in the analysis and design of switching circuits

pos: History of computing hardware eventually superseded by much faster all-electric computers, originally using vacuum tubes. The Z2 was one of the earliest examples of an electromechanical relay computer, and was created by German engineer Konrad Zuse in 1940. It was an improvement on his earlier Z1; although it used the same mechanical memory, it replaced the arithmetic and control logic with electrical relay circuits. In the same year, electro-mechanical devices called bombes were built by British cryptologists to help decipher German Enigma-machine-encrypted secret messages during World War II. The bombes' initial design was created in 1939 at the UK Government Code and Cypher School

pos: Computer architecture Computer architecture In computer engineering, computer architecture is a set of rules and methods that describe the functionality, organization, and implementation of computer systems. Some definitions of architecture define it as describing the capabilities and programming model of a computer but not a particular implementation. In other definitions computer architecture involves instruction set architecture design, microarchitecture design, logic design, and implementation. The first documented computer architecture was in the correspondence between Charles Babbage and Ada Lovelace, describing the analytical engine. When building the computer Z1 in 1936, Konrad Zuse described in two patent applications for his future projects that machine

neg: Z3 (computer) Shannon's work and developed the groundwork independently for his first computer Z1 which he designed and built from 1935 to 1938. Zuse's coworker Helmut Schreyer built an electronic digital experimental model of a computer using 100 vacuum tubes in 1942, but it was lost at the end of the war. An analog computer was built by the rocket scientist Helmut Hölzer in 1942 at the Peenemünde Army Research Center to calculate and simulate V-2 rocket trajectories. The Tommy Flowers-built Colossus (1943) and the Atanasoff–Berry Computer (1942) used thermionic valves (vacuum tubes) and binary representation of numbers. Programming was by means

neg: Z1 (computer) with the instructions encoded in punched holes. "Z1 was a machine of about 1000 kg weight, which consisted from some 20000 parts. It was a programmable computer, based on binary floating-point numbers and a binary switching system. It consisted completely of thin metal sheets, which Zuse and his friends produced using a jigsaw." "The [data] input device was a keyboard...The Z1’s programs (Zuse called them Rechenpläne) were stored on punch tapes by means of an 8-bit code" Construction of the Z1 was privately financed. Zuse got money from his parents, his sister Lieselotte, some students of the fraternity "AV Motiv"

neg: Konrad Zuse 10, the street leading up the Kreuzberg, Berlin. Working in his parents' apartment in 1936, he produced his first attempt, the Z1, a floating point binary mechanical calculator with limited programmability, reading instructions from a perforated 35 mm film. In 1937, Zuse submitted two patents that anticipated a von Neumann architecture. He finished the Z1 in 1938. The Z1 contained some 30,000 metal parts and never worked well due to insufficient mechanical precision. On 30 January 1944, the Z1 and its original blueprints were destroyed with his parents' flat and many neighbouring buildings by a British air raid in World

neg: Z1 (computer) the clock frequency of 1 Hz (cycle per second) to the machine. 'The memory was constructed from thin strips of slotted metal and small pins, and proved faster, smaller, and more reliable, than relays. The Z2 used the mechanical memory of the Z1, but used relay-based arithmetic. The Z3 was experimentally built entirely of relays. The Z4 was the first attempt at a commercial computer, reverting to the faster and more economical mechanical slotted metal strip memory, with relay processing, of the Z2, but the war interrupted the Z4 development.' The Z1 was never very reliable in operation due to

neg: Qubit procedure is now known as Schumacher compression. A binary digit, characterized as 0 and 1, is used to represent information in classical computers. A binary digit can represent up to one bit of Shannon information, where a bit is the basic unit of information. However, in this article, the word bit is synonymous with binary digit. In classical computer technologies, a "processed" bit is implemented by one of two levels of low DC voltage, and whilst switching from one of these two levels to the other, a so-called forbidden zone must be passed as fast as possible, as electrical voltage

neg: Punched card "1" in a signed numeric column, or an unsigned digit "1" in a column where the "12" has some other use. The introduction of EBCDIC in 1964 defined columns with as many as six punches (zones [12,11,0,8,9] + digit [1–7]). IBM and other manufacturers used many different 80-column card character encodings. A 1969 American National Standard defined the punches for 128 characters and was named the "Hollerith Punched Card Code" (often referred to simply as "Hollerith Card Code"), honoring Hollerith. For some computer applications, binary formats were used, where each hole represented a single binary digit (or "bit"), every column

neg: Z1 (computer) was the first in a series of computers that Zuse designed. Its original name was "V1" for VersuchsModell 1 (meaning Experimental Model 1). After WW2, it was renamed "Z1" to differentiate from the flying bombs designed by Robert Lusser. The Z2 and Z3 were follow-ups based on many of the same ideas as the Z1. The Z1 contained almost all the parts of a modern computer, i.e. control unit, memory, micro sequences, floating-point logic and input–output devices. The Z1 was freely programmable via punched tape and a punched tape reader. There was a clear separation between the punched tape reader,

neg: Guard digit the intermediate calculation, we say there are "M−N" guard digits. Guard digits are also used in floating point operations in most computer systems. Given formula_1 we have to line up the binary points. This means we must add an extra digit to the first operand—a guard digit. This gives us formula_2. Performing this operation gives us formula_3 or formula_4. Without using a guard digit we have formula_5, yielding formula_6 or formula_7. This gives us a relative error of 1. Therefore, we can see how important guard digits can be. An example of the error caused by floating point roundoff is

neg: Ternary computer point nil". Virtual Adepts in the roleplaying game "" use ternary computers. In Howard Tayler's webcomic "Schlock Mercenary", every modern computer is a ternary computer. AIs use the extra digit as "maybe" in boolean (true/false) operations, thus having a much more intimate understanding of fuzzy logic than is possible with binary computers. The Conjoiners, in Alastair Reynolds' "Revelation Space" series, use ternary logic to program their computers and nanotechnology devices. Ternary computer A ternary computer (also called trinary computer) is a computer that uses ternary logic (three possible values) instead of the more popular binary system ("Base 2") in its

neg: Computer number format sixteen values, a nibble is sometimes known as a hexadecimal digit. Octal and hex are convenient ways to represent binary numbers, as used by computers. Computer engineers often need to write out binary quantities, but in practice writing out a binary number such as 1001001101010001 is tedious and prone to errors. Therefore, binary quantities are written in a base-8, or "octal", or, much more commonly, a base-16, "hexadecimal" or "hex", number format. In the decimal system, there are 10 digits, 0 through 9, which combine to form numbers. In an octal system, there are only 8 digits, 0 through 7.

neg: Check digit Check digit A check digit is a form of redundancy check used for error detection on identification numbers, such as bank account numbers, which are used in an application where they will at least sometimes be input manually. It is analogous to a binary parity bit used to check for errors in computer-generated data. It consists of one or more digits computed by an algorithm from the other digits (or letters) in the sequence input. With a check digit, one can detect simple errors in the input of a series of characters (usually digits) such as a single mistyped digit

neg: Decimal computer processors, and also the Intel x86 family have special instructions that support conversion to and from BCD. The Psion Organiser I handheld computer’s manufacturer-supplied software implemented its floating point operations in software using BCD entirely. All later Psion models used binary only, rather than BCD. Decimal arithmetic is now becoming more common; for instance, three decimal types with two binary encodings were added to the 2008 IEEE 754r standard, with 7-, 16-, and 34-digit decimal significands. The IBM Power6 processor and the IBM System z9 have implemented these types using the Densely Packed Decimal binary encoding, the first in hardware

neg: Finger binary (see below the illustrations.): The rightmost digit represents two to the zeroth power (i.e., it is the "ones digit"); the digit to its left represents two to the first power (the "twos digit"); the next digit to the left represents two to the second power (the "fours digit"); and so on. (The decimal number system is essentially the same, only that powers of ten are used: "ones digit", "tens digit" "hundreds digit", etc.) It is possible to use anatomical digits to represent numerical digits by using a raised finger to represent a binary digit in the "1" state and a

neg: Numerical digit rod numerals. The binary (base 2), octal (base 8), and hexadecimal (base 16) systems, extensively used in computer science, all follow the conventions of the Hindu–Arabic numeral system. The binary system uses only the digits "0" and "1", while the octal system uses the digits from "0" through "7". The hexadecimal system uses all the digits from the decimal system, plus the letters "A" through "F", which represent the numbers 10 to 15 respectively. The ternary and balanced ternary systems have sometimes been used. They are both base 3 systems. Balanced ternary is unusual in having the digit values 1,

neg: Karatsuba algorithm operands with fewer than "n" digits. Therefore, those products can be computed by recursive calls of the Karatsuba algorithm. The recursion can be applied until the numbers are so small that they can (or must) be computed directly. In a computer with a full 32-bit by 32-bit multiplier, for example, one could choose "B" = 2 = , and store each digit as a separate 32-bit binary word. Then the sums "x" + "x" and "y" + "y" will not need an extra binary word for storing the carry-over digit (as in carry-save adder), and the Karatsuba recursion can be

neg: History of general-purpose CPUs core memory which provided higher speeds. Hard disks were also starting to grow popular. A computer is an automatic abacus. The type of number system affects the way it works. In the early 1950s most computers were built for specific numerical processing tasks, and many machines used decimal numbers as their basic number system; that is, the mathematical functions of the machines worked in base-10 instead of base-2 as is common today. These were not merely binary coded decimal (BCD). Most machines had ten vacuum tubes per digit in each processor register. Some early Soviet computer designers implemented systems based

neg: Check digit 10 to calculate the check digit (or left as-is if already zero). A GS1 check digit calculator and detailed documentation is online at GS1's website. Another official calculator page shows that the mechanism for GTIN-13 is the same for Global Location Number/GLN. Notable algorithms include: Check digit A check digit is a form of redundancy check used for error detection on identification numbers, such as bank account numbers, which are used in an application where they will at least sometimes be input manually. It is analogous to a binary parity bit used to check for errors in computer-generated data. It

neg: HCP Z1 HCP Z1 HCP Z1 - is a series of train carriages constructed by H. Cegielski in Poznań, which meet the UIC-Z1 standard for passenger train carriages. Several types of the wagons in the standard have been built, with over 100 units built. The main user of the carriages is PKP Intercity. The HCP Z1 is also used by the Belarusian Railway and the Polski Tabor Szynowy. At the end of the 1970s, the first plans have been drawn up for passenger carriages "with increased comfort" (127A i 127Aa) which have the form of the UIC-Z2. The first two units of

neg: Binary number Binary number In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically 0 (zero) and 1 (one). The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computers and computer-based devices. The modern binary number system was studied in Europe in the 16th and 17th centuries by Thomas Harriot, Juan Caramuel

neg: Ternary computer Ternary computer A ternary computer (also called trinary computer) is a computer that uses ternary logic (three possible values) instead of the more popular binary system ("Base 2") in its calculations. One early calculating machine, built by Thomas Fowler entirely from wood in 1840, operated in balanced ternary. The first modern, electronic ternary computer Setun was built in 1958 in the Soviet Union at the Moscow State University by Nikolay Brusentsov, and it had notable advantages over the binary computers which eventually replaced it, such as lower electricity consumption and lower production cost. In 1970 Brusentsov built an enhanced version

neg: Binary number and overflow is repeated for each digit of significance. Counting progresses as follows: Binary counting follows the same procedure, except that only the two symbols "0" and "1" are available. Thus, after a digit reaches 1 in binary, an increment resets it to 0 but also causes an increment of the next digit to the left: In the binary system, each digit represents an increasing power of 2, with the rightmost digit representing 2, the next representing 2, then 2, and so on. The equivalent decimal representation of a binary number is sum of the powers of 2 which each

neg: Little man computer of decimal numbers was chosen to minimize the complexity for students who may not be comfortable working in binary/hexadecimal. Some LMC simulators are programmed directly using 3-digit numeric instructions and some use 3-letter mnemonic codes and labels. In either case, the instruction set is deliberately very limited ("typically about ten instructions") to simplify understanding. If the LMC uses mnemonic codes and labels then these are converted into 3-digit numeric instructions when the program is assembled. The table below shows a typical numeric instruction set and the equivalent mnemonic codes. This program (instruction 901 to instruction 000) is written just using

neg: Binary number binary digits to represent an octal digit). The correspondence between octal and binary numerals is the same as for the first eight digits of hexadecimal in the table above. Binary 000 is equivalent to the octal digit 0, binary 111 is equivalent to octal 7, and so forth. Converting from octal to binary proceeds in the same fashion as it does for hexadecimal: And from binary to octal: And from octal to decimal: Non-integers can be represented by using negative powers, which are set off from the other digits by means of a radix point (called a decimal point in

neg: Binary number through each symbol, in increasing order. Before examining binary counting, it is useful to briefly discuss the more familiar decimal counting system as a frame of reference. Decimal counting uses the ten symbols "0" through "9". Counting begins with the incremental substitution of the least significant digit (rightmost digit) which is often called the "first digit". When the available symbols for this position are exhausted, the least significant digit is reset to "0", and the next digit of higher significance (one position to the left) is incremented ("overflow"), and incremental substitution of the low-order digit resumes. This method of reset

neg: ICT 1301 clock cycles per digit; and division was performed in software. The computer was announced in May 1960. The first customer delivery was in 1962, a 1301 sold to the University of London. About 150 to 200 of these machines were sold. One of their main attractions was that they performed British currency calculations (pounds, shillings and pence) in hardware. They also had the advantage of programmers not having to learn binary or octal arithmetic as the instruction set was pure decimal and the arithmetic unit had no binary mode, only decimal or pounds, shillings and pence. The London University machine

neg: German destroyer Z1 Leberecht Maass charges carried. Mine rails could be fitted on the rear deck that had a maximum capacity of 60 mines. A system of passive hydrophones designated as 'GHG' ("Gruppenhorchgerät") was fitted to detect submarines. Z1 "Leberecht Maass", named after Rear Admiral ("Konteradmiral") Leberecht Maass, who was killed while commanding German forces in the Battle of Heligoland Bight in August 1914, was the first destroyer to be built in Germany since World War I. She was ordered on 7 July 1934 and laid down at Deutsche Werke, Kiel, on 10 October 1934 as yard number K232. The ship was launched on 18

neg: Balanced ternary bases have been discussed by John Colson, John Leslie, Augustin-Louis Cauchy, and possibly even the ancient Indian Vedas. In the early days of computing, a few experimental Soviet computers were built with balanced ternary instead of binary, the most famous being the Setun, built by Nikolay Brusentsov and Sergei Sobolev. The notation has a number of computational advantages over traditional binary and ternary. Particularly, the plus–minus consistency cuts down the carry rate in multi-digit multiplication, and the rounding–truncation equivalence cuts down the carry rate in rounding on fractions. The one-digit multiplication table has no carries in balanced ternary, and the

neg: Skew binary number system Skew binary number system The skew binary number system is a non-standard positional numeral system in which the "n"th digit contributes a value of formula_1 times the digit (digits are indexed from 0) instead of formula_2 times as they do in binary. Each digit has a value of 0, 1, or 2. Notice that a number can have many skew binary representations. For example, a decimal number 15 can be written as 1000, 201 and 122. Each number can be written uniquely in skew binary canonical form where there is only at most one instance of the digit 2, which

neg: First Draft of a Report on the EDVAC between -1 and 1 and therefore computation problems must be scaled accordingly. Vacuum tubes are to be used rather than relays due to tubes’ ability operate in one microsecond vs 10 milliseconds for relays. Von Neumann suggests (Sec. 5.6) keeping the computer as simple as possible, avoiding any attempt at improving performance by overlapping operations. Arithmetic operations are to be performed one binary digit at a time. He estimates addition of two binary digits as taking one microsecond and that therefore a 30-bit multiplication should take about 30 microseconds or about one millisecond, much faster than any computing device available

neg: Punched card input/output more "stackers" for cards read or punched. A function called "stacker select" allows the controlling computer to choose which stacker a card just read or punched will be placed into. Documation Inc., of Melbourne, Florida, made card readers for minicomputers in the 1970s: Their card readers have been used in elections, including the 2000 "Chads" election in Florida. For some computer applications, binary formats were used, where each hole represented a single binary digit (or "bit"), every column (or row) is treated as a simple bitfield, and every combination of holes is permitted. For example, the IBM 711 card reader

neg: Decimal computer and the second in microcode. Decimal computer Decimal computers are computers which can represent numbers and addresses in decimal as well as providing instructions to operate on those numbers and addresses directly in decimal, without conversion to a pure binary representation. Some also had a variable wordlength, which enabled operations on numbers with a large number of digits. Early computers that were exclusively decimal include the ENIAC, IBM NORC, IBM 650, IBM 1620, IBM 7070. In these machines, the basic unit of data was the decimal digit, encoded in one of several schemes, including binary-coded decimal or BCD, bi-quinary, excess-3,

neg: Decimal computer Decimal computer Decimal computers are computers which can represent numbers and addresses in decimal as well as providing instructions to operate on those numbers and addresses directly in decimal, without conversion to a pure binary representation. Some also had a variable wordlength, which enabled operations on numbers with a large number of digits. Early computers that were exclusively decimal include the ENIAC, IBM NORC, IBM 650, IBM 1620, IBM 7070. In these machines, the basic unit of data was the decimal digit, encoded in one of several schemes, including binary-coded decimal or BCD, bi-quinary, excess-3, and two-out-of-five code. Except for

neg: Parametron transistors due to differences in speed. Parametron Parametron is a logic circuit element invented by Eiichi Goto in 1954. The parametron is essentially a resonant circuit with a nonlinear reactive element which oscillates at half the driving frequency. The oscillation can be made to represent a binary digit by the choice between two stationary phases π radians (180 degrees) apart. Parametrons were used in early Japanese computers from 1954 through the early 1960s. A prototype parametron-based computer, the PC-1, was built at the University of Tokyo in 1958. Parametrons were used in early Japanese computers due to being reliable and

neg: Parametron Parametron Parametron is a logic circuit element invented by Eiichi Goto in 1954. The parametron is essentially a resonant circuit with a nonlinear reactive element which oscillates at half the driving frequency. The oscillation can be made to represent a binary digit by the choice between two stationary phases π radians (180 degrees) apart. Parametrons were used in early Japanese computers from 1954 through the early 1960s. A prototype parametron-based computer, the PC-1, was built at the University of Tokyo in 1958. Parametrons were used in early Japanese computers due to being reliable and inexpensive but were ultimately surpassed by

neg: John Tukey latter. Though he believed in the utility of separating the two types of analysis, he pointed out that sometimes, especially in natural science, this was problematic and termed such situations uncomfortable science. A. D. Gordon offered the following summary of Tukey's principles for statistical practice: Tukey coined many statistical terms that have become part of common usage, but the two most famous coinages attributed to him were related to computer science. While working with John von Neumann on early computer designs, Tukey introduced the word "bit" as a contraction of "binary digit". The term "bit" was first used in an

neg: Binary number found with a sum of a finite number of inverse powers of two, the zeros and ones in the binary representation of 1/3 alternate forever. Arithmetic in binary is much like arithmetic in other numeral systems. Addition, subtraction, multiplication, and division can be performed on binary numerals. The simplest arithmetic operation in binary is addition. Adding two single-digit binary numbers is relatively simple, using a form of carrying: Adding two "1" digits produces a digit "0", while 1 will have to be added to the next column. This is similar to what happens in decimal when certain single-digit numbers are

neg: German destroyer Z1 Leberecht Maass German destroyer Z1 Leberecht Maass The German destroyer Z1 "Leberecht Maass" was the lead ship of her class of four destroyers built for the German Navy (initially called the "Reichsmarine" and then renamed as the "Kriegsmarine" in 1935) during the mid-1930s. Completed in 1937, two years before the start of World War II, the ship served as a flagship and spent most of her time training although she did participate in the occupation of Memel in early 1939. Several days after the start of the war in September 1939, Z1 "Leberecht Maass" and another destroyer unsuccessfully attacked Polish ships in

neg: Binary multiplier most of their time multiplying, digital signal processor designers sacrifice a lot of chip area in order to make the multiply as fast as possible; a single-cycle multiply–accumulate unit often used up most of the chip area of early DSPs. The method taught in school for multiplying decimal numbers is based on calculating partial products, shifting them to the left and then adding them together. The most difficult part is to obtain the partial products, as that involves multiplying a long number by one digit (from 0 to 9): A binary computer does exactly the same, but with binary numbers.

neg: Bit may be used even within the same device or program. The length of a binary number may be referred to as its bit-length. In information theory, one bit is typically defined as the information entropy of a binary random variable that is 0 or 1 with equal probability, or the information that is gained when the value of such a variable becomes known. Confusion often arises because the words bit and binary digit are used interchangeably. But, within Shannon's information theory, a bit and a binary digit are fundamentally different types of entities. A binary digit is a number that

neg: Skew binary number system must be the first non-zero least significant digit. In this case 15 is written canonically as 1000. Skew binary representations of the numbers from 0 to 15 are shown in following table: The advantage of skew binary is that each increment operation can be done with at most one carry operation. This exploits the fact that formula_3. Incrementing a skew binary number is done by setting the only two to a zero and incrementing the next digit from zero to one or one to two. When numbers are represented using a form of run-length encoding as linked lists of the

neg: Digit sum algorithms to check the arithmetic operations of early computers. Earlier, in an era of hand calculation, suggested using sums of 50 digits taken from mathematical tables of logarithms as a form of random number generation; if one assumes that each digit is random, then by the central limit theorem, these digit sums will have a random distribution closely approximating a Gaussian distribution. The digit sum of the binary representation of a number is known as its Hamming weight or population count; algorithms for performing this operation have been studied, and it has been included as a built-in operation in some

neg: Binary number a separate "subtract" operation. Using two's complement notation subtraction can be summarized by the following formula: A − B = A + not B + 1 Multiplication in binary is similar to its decimal counterpart. Two numbers and can be multiplied by partial products: for each digit in , the product of that digit in is calculated and written on a new line, shifted leftward so that its rightmost digit lines up with the digit in that was used. The sum of all these partial products gives the final result. Since there are only two digits in binary, there are

neg: Hexadecimal shows the conversion of a binary number to decimal, mapping each digit to the decimal value, and adding the results. Compare this to the conversion to hexadecimal, where each group of four digits can be considered independently, and converted directly: The conversion from hexadecimal to binary is equally direct. Although quaternary (base 4) is little used, it can easily be converted to and from hexadecimal or binary. Each hexadecimal digit corresponds to a pair of quaternary digits and each quaternary digit corresponds to a pair of binary digits. In the above example 5 E B 5 2 = 11 32

neg: Bit inverse ratio, this value, approximately 3/10, but slightly more, corresponds to the fact that 2 = 1024 ~ 1000 = 10: ten binary digits are slightly more information than three decimal digits, so one binary digit is slightly more than 3/10 decimal digits. Some authors also define a binit as an arbitrary information unit equivalent to some fixed but unspecified number of bits. Bit The bit (a portmanteau of binary digit) is a basic unit of information used in computing and digital communications. A binary digit can have only one of two values, and may be physically represented with a

neg: Binary clock Each column represents a single decimal digit, a format known as binary-coded decimal (BCD). The bottom row in each column represents 1 (or 2), with each row above representing higher powers of two, up to 2 (or 8). To read each individual digit in the time, the user adds the values that each illuminated LED represents, then reads these from left to right. The first two columns represent the hour, the next two represent the minute and the last two represent the second. Since zero digits are not illuminated, the positions of each digit must be memorized if the clock

neg: Quaternary numeral system is a power of 4, conversion between these bases can be implemented by matching each hexadecimal digit with 2 quaternary digits. In the above example, Although octal and hexadecimal are widely used in computing and computer programming in the discussion and analysis of binary arithmetic and logic, quaternary does not enjoy the same status. Although quaternary has limited practical use, it can be helpful if it is ever necessary to perform hexadecimal arithmetic without a calculator. Each hexadecimal digit can be turned into a pair of quaternary digits, and then arithmetic can be performed relatively easily before converting the end

neg: Signed number representations signed integers. Another approach is to give each digit a sign, yielding the signed-digit representation. For instance, in 1726, John Colson advocated reducing expressions to "small numbers", numerals 1, 2, 3, 4, and 5. In 1840, Augustin Cauchy also expressed preference for such modified decimal numbers to reduce errors in computation. Signed number representations In computing, signed number representations are required to encode negative numbers in binary number systems. In mathematics, negative numbers in any base are represented by prefixing them with a minus ("−") sign. However, in computer hardware, numbers are represented only as sequences of bits, without extra

neg: Ternary computer of the computer, which he called Setun-70. In the USA, the ternary computing emulator Ternac working on a binary machine was developed in 1973. The ternary computer QTC-1 was developed in Canada. Ternary computing is commonly implemented in terms of balanced ternary, which uses the three digits −1, 0, and +1. The negative value of any balanced ternary digit can be obtained by replacing every + with a − and vice versa. It is easy to subtract a number by inverting the + and − digits and then using normal addition. Balanced ternary can express negative values as easily as

neg: Consensus (computer science) Varying models of computation may define a "consensus problem". Some models may deal with fully connected graphs, while others may deal with rings and trees. In some models message authentication is allowed, whereas in others processes are completely anonymous. Shared memory models in which processes communicate by accessing objects in shared memory are also an important area of research. A special case of the consensus problem, called binary consensus, restricts the input, and hence the output domain, to a single binary digit {0,1}. There are two types of failures a process may undergo, a crash failure or a Byzantine failure.

neg: Computer number format calculations are carried out with number formats that fit into a processor register, but some software systems allow representation of arbitrarily large numbers using multiple words of memory. Computers represent data in sets of binary digits. The representation is composed of bits, which in turn are grouped into larger sets such as bytes. A "bit" is a binary digit that represents one of two states. The concept of a bit can be understood as a value of either "1" or "0", "on" or "off", "yes" or "no", "true" or "false", or encoded by a switch or toggle of some kind.

neg: HCP Z1 their route in the half of June 2014. Another 3 167A passenger carriages were successfully delivered in July 2014, which made the second depot for the PKP Intercity " Przemysław". Altogether 4 batches of passenger carriages have been delivered which included an additional buffet carriage. HCP Z1 HCP Z1 - is a series of train carriages constructed by H. Cegielski in Poznań, which meet the UIC-Z1 standard for passenger train carriages. Several types of the wagons in the standard have been built, with over 100 units built. The main user of the carriages is PKP Intercity. The HCP Z1 is

neg: Computer number format and 0F8H or 0xf8 for hexadecimal numbers. Each of these number systems are positional systems, but while decimal weights are powers of 10, the octal weights are powers of 8 and the hex weights are powers of 16. To convert from hex or octal to decimal, for each digit one multiplies the value of the digit by the value of its position and then adds the results. For example: formula_1 formula_2 formula_3 formula_4 formula_5 formula_6 formula_7 formula_8 formula_9 formula_10 Fixed-point formatting can be useful to represent fractions in binary. The number of bits needed for the precision and range desired

neg: Integer (computer science) "false" and "true" respectively. This type can be stored in memory using a single bit, but is often given a full byte for convenience of addressing and speed of access. A four-bit quantity is known as a "nibble" (when eating, being smaller than a "bite") or "nybble" (being a pun on the form of the word "byte"). One nibble corresponds to one digit in hexadecimal and holds one digit or a sign code in binary-coded decimal. The term "byte" initially meant 'the smallest addressable unit of memory'. In the past, 5-, 6-, 7-, 8-, and 9-bit bytes have all been

neg: Z1 (computer) (cf. Helmut Schreyer) and Kurt Pannke (a calculating machines manufacturer in Berlin) to do so. Zuse constructed the Z1 in his parents' apartment; in fact, he was allowed to use the living room for his construction. In 1936, Zuse quit his job in airplane construction in order to build the Z1. Zuse is said to have used "thin metal strips" and perhaps "metal cylinders" or glass plates to construct Z1. There were probably no commercial relays in it (although the Z3 is said to have used a few telephone relays). The only electrical unit was an electric motor to give

neg: HCP Z1 the carriage have been built by PaFaWag in 1980. The structure and use of the carriages have been drawn up by the H. Cegielski company to build the upcoming Z2. With the use of the plans of the 127A in Poznań warehouses to house the manufacture have been built where the 134Aa/b have been built. The first Z1 carriages in Poland were built by Adtranz/ABB. In the third quarter of 1996 the first 15 carriages of the ABB Z1A standard class have been delivered to PKP, later (after the first quarter of 1997) 35 carriages of the ABB Z1B have

neg: Mechanical calculator accommodate shillings and pence, extra columns were added for the tens digit[s], 10 and 20 for shillings, and 10 for pence. Of course, these functioned as radix-20 and radix-12 mechanisms. A variant of the Marchant, called the Binary-Octal Marchant, was a radix-8 (octal) machine. It was sold to check very early vacuum-tube (valve) binary computers for accuracy. (Back then, the mechanical calculator was much more reliable than a tube/valve computer.) As well, there was a twin Marchant, comprising two pinwheel Marchants with a common drive crank and reversing gearbox. Twin machines were relatively rare, and apparently were used for surveying

neg: Ternary computer positive ones, without the need for a leading negative sign as with decimal numbers. These advantages make some calculations more efficient in ternary than binary. Considering that digit signs are mandatory, and nonzero digits are magnitude 1 only, notation using only zero and signs alone is more concise than when 1's are used. With the advent of mass-produced binary components for computers, ternary computers have diminished in significance. However, Donald Knuth argues that they will be brought back into development in the future to take advantage of ternary logic's elegance and efficiency. One possible way this could happen is by

neg: Hexadecimal Hexadecimal In mathematics and computing, hexadecimal (also base , or hex) is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A–F (or alternatively a–f) to represent values ten to fifteen. Hexadecimal numerals are widely used by computer system designers and programmers, as they provide a more human-friendly representation of binary-coded values. Each hexadecimal digit represents four binary digits, also known as a nibble, which is half a byte. For example, a single byte can have values ranging from 0000 0000

neg: Computer and had longer, indefinite, service life. Transistorized computers could contain tens of thousands of binary logic circuits in a relatively compact space. At the University of Manchester, a team under the leadership of Tom Kilburn designed and built a machine using the newly developed transistors instead of valves. Their first transistorised computer and the first in the world, was operational by 1953, and a second version was completed there in April 1955. However, the machine did make use of valves to generate its 125 kHz clock waveforms and in the circuitry to read and write on its magnetic drum memory,

neg: Z1 (computer) the control unit for supervising the whole machine and the execution of the instructions, the arithmetic unit, and the input and output devices. The input tape unit read perforations in 35-millimeter film. The Z1 was a 22-bit floating-point value adder and subtracter, with some control logic to make it capable of more complex operations such as multiplication (by repeated additions) and division (by repeated subtractions). The Z1's instruction set had nine instructions and it took between one and twenty cycles per instruction. The Z1 had a 64-word floating-point memory, where each word of memory could be read from – and

neg: Redundant binary representation Redundant binary representation A redundant binary representation (RBR) is a numeral system that uses more bits than needed to represent a single binary digit so that most numbers have several representations. An RBR is unlike usual binary numeral systems, including two's complement, which use a single bit for each digit. Many of an RBR's properties differ from those of regular binary representation systems. Most importantly, an RBR allows addition without using a typical carry. When compared to non-redundant representation, an RBR makes bitwise logical operation slower, but arithmetic operations are faster when a greater bit width is used. Usually, each

neg: Binary number 5 is 5, with a remainder of 2. The process of taking a binary square root digit by digit is the same as for a decimal square root, and is explained here. An example is: Though not directly related to the numerical interpretation of binary symbols, sequences of bits may be manipulated using Boolean logical operators. When a string of binary symbols is manipulated in this way, it is called a bitwise operation; the logical operators AND, OR, and XOR may be performed on corresponding bits in two binary numerals provided as input. The logical NOT operation may be performed

neg: Extended precision digit is the eighteenth fractional digit and thus the twentieth significant digit of the string. Bounds on conversion between decimal and binary for the 80-bit format can be given as follows: if a decimal string with at most 18 significant digits is correctly rounded to an 80-bit IEEE 754 binary floating point value (as on input) then converted back to the same number of significant decimal digits (as for output), then the final string will exactly match the original; while, conversely, if an 80-bit IEEE 754 binary floating point value is correctly converted and (nearest) rounded to a decimal string

neg: Bit Bit The bit (a portmanteau of binary digit) is a basic unit of information used in computing and digital communications. A binary digit can have only one of two values, and may be physically represented with a two-state device. These state values are most commonly represented as either a . The two values of a binary digit can also be interpreted as logical values (true/false, yes/no), algebraic signs (+/−), activation states (on/off), or any other two-valued attribute. The correspondence between these values and the physical states of the underlying storage or device is a matter of convention, and different assignments

neg: Burroughs Medium Systems binary-coded decimal BCD digits per byte. Portable COBOL programs did not use binary integers at all, so the B2500 did not either, not even for memory addresses. Memory was addressed down to the 4-bit digit in big-endian style, using 5-digit decimal addresses. Floating point numbers also used base 10 rather than some binary base, and had up to 100 mantissa digits. A typical COBOL statement 'ADD A, B GIVING C' may use operands of different lengths, different digit representations, and different sign representations. This statement compiled into a single 12-byte instruction with 3 memory operands. Complex formatting for printing was

neg: 4-bit single-digit hexadecimal numbers can be written with four bits. Binary-coded decimal is a digital encoding method for numbers using decimal notation, with each decimal digit represented by four bits. 4-bit Some of the first microprocessors had a 4-bit word length and were developed around 1970. The TMS 1000, the world's first single-chip microprocessor, was a 4-bit CPU; it had a Harvard architecture, with an on-chip instruction ROM, 8-bit-wide instructions and an on-chip data RAM with 4-bit words. The first commercial microprocessor was the binary-coded decimal (BCD-based) Intel 4004, developed for calculator applications in 1971; it had a 4-bit word length,

neg: Finger binary Finger binary Finger binary is a system for counting and displaying binary numbers on the fingers of one or more hands. It is possible to count from 0 to 31 (2−1) using the fingers of a single hand, or from 0 through 1023 (2−1) if both hands are used. In the binary number system, each numerical digit has two possible states (0 or 1) and each successive digit represents an increasing power of two. Note: What follows is but one of several possible schemes for assigning the values 1, 2, 4, 8, 16, etc. to fingers, not necessarily the best.

neg: Finger binary people will find it difficult to hold all fingers independently (especially the middle and ring fingers) in more than two distinct positions. Finger binary Finger binary is a system for counting and displaying binary numbers on the fingers of one or more hands. It is possible to count from 0 to 31 (2−1) using the fingers of a single hand, or from 0 through 1023 (2−1) if both hands are used. In the binary number system, each numerical digit has two possible states (0 or 1) and each successive digit represents an increasing power of two. Note: What follows is

neg: Redundant binary representation time proportional to log("n") (where "n" is the number of digit) compared to a constant-time in two's complement. It is, however, possible to "partially" convert only the least-significant portion of a redundantly represented number to non-redundant form. This allows operations such as masking off the low "k" bits can be done in log("k") time. Redundant binary representation A redundant binary representation (RBR) is a numeral system that uses more bits than needed to represent a single binary digit so that most numbers have several representations. An RBR is unlike usual binary numeral systems, including two's complement, which use a single

neg: German locomotive classification DB system, the DR decided to use the first digit 1 for diesel and the first digit 2 for electric vehicles (including both locomotives and multiple units/railcars). Therefore, e. g. the DRG-built E 44 class was renumbered 144 by the DB and 244 by the DR. To avoid clashes between steam and electric/diesel unit numbers (the space separating class and ordering number being non-significant in computer processing), steam locomotive class numbers in the 10-19 and 20-29 number ranges were reassigned to the 01-09 and 30-39 number ranges, respectively (e. g. the steam locomotive with the old number "23 1046", built

neg: HCP Z1 first, then the 11ANc. The first serial producer of the UIC-Z1 in Poland became H. Cegielski. In the beginning it was believed the Polish company would register the carriages under the ABB Henschel company, but they decided to build the carriages with their own structure of the 145A and 145Ab. On the 31 December 1997 the company had completed their first 6 units of the 152A type and not long after the open saloon second class carriages 154A have been built. In 2000 two business class carriages of the 145Ac have been built and the first sleep carriage of the

neg: Williams tube around the dot where those electrons land. The resulting charge well remains on the surface of the tube for a fraction of a second while the electrons flow back to their original locations. The lifetime depends on the electrical resistance of the phosphor and the size of the well. The process of creating the charge well is used as the write operation in a computer memory, storing a single binary digit, or bit. A collection of dots or spaces, often one horizontal row on the display, represents a computer word. There is a relationship between the size and spacing of

neg: Computer of these parts are thousands to trillions of small electrical circuits which can be turned off or on by means of an electronic switch. Each circuit represents a bit (binary digit) of information so that when the circuit is on it represents a "1", and when off it represents a "0" (in positive logic representation). The circuits are arranged in logic gates so that one or more of the circuits may control the state of one or more of the other circuits. When unprocessed data is sent to the computer with the help of input devices, the data is processed

neg: MSI Barcode MSI barcode for the number sequence 1234567 using the most common Mod 10 check digit methodology. The check digit (as calculated above) for this sequence is 4. Once you have calculated your check digit, simply map each character in the string to be encoded using the table above as a reference to get the binary map of the bar code; remember to precede the code with "start" and to end it with "stop" For example, to map the string 1234567 with a Mod 10 check digit it would produce the following binary map: This results in the following barcode: MSI

neg: Digital electronic computer machines for computation and communicating using natural language. A digital computer can perform its operations in the decimal system, in binary, in ternary or in other numeral systems. As of 2014, all digital electronic computers commonly used, whether personal computers or supercomputers, are working in the binary number system and also use binary logic. A few ternary computers using ternary logic were built mainly in the Soviet Union as research projects. A digital electronic computer is not necessarily a transistorized computer: before the advent of the transistor, computers used vacuum tubes. The transistor enabled electronic computers to become much more

neg: Trams in Melbourne the C, D and E class trams; the last Z1-class withdrawn on 23 April 2016. Many were later sold at auctions, while others were donated to tram museums. In 1978 and 1979, fifteen Z2-class trams, having little difference from the Z1-class, were built. As with the Z1-class, the Z2-class trams have been withdrawn from service. From 1979 to 1984, Z3-class trams were introduced. They have an additional door on each side of the tram, no conductor's console was provided, and smoother acceleration and braking compared to the Z1-class. 115 were built, 112 of which are in service. The A-class trams

neg: Normalized number a number to base two and normalizing it are the first steps in storing a real number as a binary floating-point number in a computer, though bases of eight and sixteen are also used. Although the point is described as "floating", for a normalised floating point number its position is fixed, the movement being reflected in the different values of the power. Normalized number In applied mathematics, a number is normalized when it is written in scientific notation with one non-zero decimal digit before the decimal point. Thus, a real number, when written out in normalized scientific notation, is as

neg: Binary number converted to binary, whereupon the first converted piece is multiplied by 10 and added to the second converted piece, where "k" is the number of decimal digits in the second, least-significant piece before conversion. Binary may be converted to and from hexadecimal more easily. This is because the radix of the hexadecimal system (16) is a power of the radix of the binary system (2). More specifically, 16 = 2, so it takes four digits of binary to represent one digit of hexadecimal, as shown in the adjacent table. To convert a hexadecimal number into its binary equivalent, simply substitute

neg: Symbol rate bit per symbol, such that binary "0" is represented by one symbol, and binary "1" by another symbol. In more advanced modems and data transmission techniques, a symbol may have more than two states, so it may represent more than one binary digit (a binary digit always represents one of exactly two states). For this reason, the baud rate value will often be lower than the gross bit rate. "Example of use and misuse of "baud rate"": It is correct to write "the baud rate of my COM port is 9,600" if we mean that the bit rate is 9,600

neg: Radix has a ones' place, tens' place, hundreds' place, and so on, radix "b" would have a ones' place, then a "b"s' place, a "b"s' place, etc. Commonly used numeral systems include: The octal and hexadecimal systems are often used in computing because of their ease as shorthand for binary. Every hexadecimal digit corresponds to a sequence of four binary digits, since sixteen is the fourth power of two; for example, hexadecimal 78 is binary . Similarly, every octal digit corresponds to a unique sequence of three binary digits, since eight is the cube of two. Radices are usually natural numbers.

neg: BCD (character encoding) the adaptation of the punched card code to a six-bit binary code by encoding the digit rows (nine rows, plus unpunched) into the low four bits, and the zone rows (three rows, plus unpunched) into the high two bits. The digit zero (a single punch in row 0) is usually handled specially in some way, and the digit code was extended to values 10 through 15 by combining a digit in the range 2–7 with a punch in row 8. IBM applied the terms "binary-coded decimal" and "BCD" to the variations of BCD "alphamerics" used in most early IBM computers,

neg: Time formatting and storage bugs 1900 problem, but it has failed to recognise people over 100 years old. The SPD EEPROM on modern computer memory modules contains a single-byte binary-coded decimal (two digit) year-of-manufacture code at offset +93 (0x5D). Due to the 18–24 month generational cycle in computer technology this should not be a problem. Some systems had problems once the year rolled over to 2010. This was dubbed by some in the media as the "Y2K+10" or "Y2.01k" problem. The main source of problems was confusion between hexadecimal number encoding and BCD encodings of numbers. The numbers 0 through 9 are encoded in both

neg: IBM 305 RAMAC the computer itself) could be programmed by inserting wire jumpers into a plugboard control panel. System architecture was documented in the "305 RAMAC Manual of Operation". The 305 was a character-oriented variable "word" length decimal (BCD) computer with a drum memory rotating at 6000 RPM that held 3200 alphanumeric characters. A core memory buffer of 100 characters was used for temporary storage during data transfers. Each character was 6 bits plus 1 odd parity bit ("R") composed of two zone bits ("X" and "O") and remaining four binary bits for the value of the digit in the following format: Instructions

neg: Clary DE-60 order. Clary Corporation was founded by Hugh L. Clary in 1939. Today the company manufactures products such as uninterruptible power supply systems. Clary DE-60 The Clary DE-60 was an early transistorized digital computer made by Clary Corporation. It was a compact (desk-sized) general-purpose computer intended for both scientific and business applications. It operated on 18-digit binary coded decimal words used fixed-point arithmetic. Main memory was a 32-word magnetic drum memory. Input and output devices included a console keyboard, printer, paper tape and punched card system. For programming, the system used sequential instructions from the keyboard and plug-boards. Custom modules for

neg: Clary DE-60 Clary DE-60 The Clary DE-60 was an early transistorized digital computer made by Clary Corporation. It was a compact (desk-sized) general-purpose computer intended for both scientific and business applications. It operated on 18-digit binary coded decimal words used fixed-point arithmetic. Main memory was a 32-word magnetic drum memory. Input and output devices included a console keyboard, printer, paper tape and punched card system. For programming, the system used sequential instructions from the keyboard and plug-boards. Custom modules for trigonometric and other functions could be installed. The system was introduced in 1959. By 1961, about 18 systems were operating or on

neg: Carry-save adder and so on to the end of the sum. Although we know the last digit of the result at once, we cannot know the first digit until we have gone through every digit in the calculation, passing the carry from each digit to the one on its left. Thus adding two "n"-digit numbers has to take a time proportional to "n", even if the machinery we are using would otherwise be capable of performing many calculations simultaneously. In electronic terms, using bits (binary digits), this means that even if we have "n" one-bit adders at our disposal, we still have

neg: Binary number numeric values may be represented by two different voltages; on a magnetic disk, magnetic polarities may be used. A "positive", "yes", or "on" state is not necessarily equivalent to the numerical value of one; it depends on the architecture in use. In keeping with customary representation of numerals using Arabic numerals, binary numbers are commonly written using the symbols 0 and 1. When written, binary numerals are often subscripted, prefixed or suffixed in order to indicate their base, or radix. The following notations are equivalent: When spoken, binary numerals are usually read digit-by-digit, in order to distinguish them from decimal