Binary Digit

1. Binary Digit https://store.theartofservice.com/the-binary-digit-toolkit.html

2. Bit • A bit is the basic unit of information in computing and digital communications. A bit can have only one of two values, and may therefore be physically implemented with a two-state device. The most common representation of these values are 0and1. The term bit is a contraction of binary digit. https://store.theartofservice.com/the-binary-digit-toolkit.html

3. Bit History • Tukey, who had written a Bell Labs memo on 9 January 1947 in which he contracted "binary digit" to simply "bit" https://store.theartofservice.com/the-binary-digit-toolkit.html

4. Bit Unit and symbol • The bit is not defined in the International System of Units (SI). However, the International Electrotechnical Commission issued standard IEC 60027, which specifies that the symbol for binary digit should be bit, and this should be used in all multiples, such as kbit, for kilobit. However, the lower-case letter b is widely used as well and was recommended by the IEEE 1541 Standard (2002). In contrast, the upper case letter B is the standard and customary symbol for byte. https://store.theartofservice.com/the-binary-digit-toolkit.html

5. Bit Information capacity and information compression • Using an analogy, the hardware binary digits refer to the amount of storage space available (like the number of buckets available to store things), and the information content the filling, which comes in different levels of granularity (fine or coarse, that is, compressed or uncompressed information) https://store.theartofservice.com/the-binary-digit-toolkit.html

6. Hexadecimal • Each hexadecimal digit represents four binary digits (bits), and the primary use of hexadecimal notation is a human-friendly of binary-coded values in computing and digital electronics. One hexadecimal digit represents a nibble, which is half of an octet or byte (8 bits). For example, byte values can range from 0 to 255 (decimal), but may be more conveniently represented as two hexadecimal digits in the range 00 to FF. Hexadecimal is also commonly used to represent computer memory addresses. https://store.theartofservice.com/the-binary-digit-toolkit.html

7. Octal • The octal amount system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Octal numerals can be made from binary numerals by grouping consecutive binary digits into groups of three (starting from the right). For example, the binary representation for decimal 74 is 1001010, which can be grouped into (00)1 001 010 – so the octal representation is 112. https://store.theartofservice.com/the-binary-digit-toolkit.html

8. Octal In computers • Octal was an ideal abbreviation of binary for these machines because their word size is divisible by three (each octal digit represents three binary digits) https://store.theartofservice.com/the-binary-digit-toolkit.html

9. Octal In computers • On such systems three octal digits per byte would be required, with the most significant octal digit representing two binary digits (plus one bit of the next significant byte, if any) https://store.theartofservice.com/the-binary-digit-toolkit.html

10. Octal Binary to octal conversion • The process is the reverse of the previous algorithm. The binary digits are grouped by threes, starting from the least significant bit and proceeding to the left and to the right. Add leading 0s (or trailing zeros to the right of decimal point) to fill out the last group of three if necessary. Then replace each trio with the equivalent octal digit. https://store.theartofservice.com/the-binary-digit-toolkit.html

11. Binary number History • In 1605 Francis Bacon discussed a system whereby letters of the alphabet could be reduced to sequences of binary digits, which could then be encoded as scarcely visible variations in the font in any random text https://store.theartofservice.com/the-binary-digit-toolkit.html

12. Binary number Representation • Any number can be represented by any sequence of bits (binary digits), which in turn may be represented by any mechanism capable of being in two mutually exclusive states. The following sequence of symbols could all be interpreted as the binary numeric value of 667: https://store.theartofservice.com/the-binary-digit-toolkit.html

13. Binary number Counting in binary • Since binary is a base-2 system, each digit represents an increasing power of 2, with the rightmost digit representing 20, the next representing 21, then 22, and so on. To determine the decimal representation of a binary number simply take the sum of the products of the binary digits and the powers of 2 which they represent. For example, the binary number 100101 is converted to decimal form as follows: https://store.theartofservice.com/the-binary-digit-toolkit.html

14. Binary number Hexadecimal • To convert a hexadecimal number into its binary equivalent, simply substitute the corresponding binary digits: https://store.theartofservice.com/the-binary-digit-toolkit.html

15. Binary number Octal • Binary is also easily converted to the octal amount system, since octal uses a radix of 8, which is a power of two (namely, 23, so it takes exactly three 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. https://store.theartofservice.com/the-binary-digit-toolkit.html

16. Boolean algebra Values • Whereas in elementary algebra expressions denote mainly numbers, in Boolean algebra they denote the truth values false and true. These values are represented with the bits (or binary digits) being 0 and 1. They do not behave like the integers 0 and 1, for which 1 + 1 = 2, but may be identified with the elements of the two-element field GF(2), for which 1 + 1 = 0 with + serving as the Boolean operation XOR. https://store.theartofservice.com/the-binary-digit-toolkit.html

17. Operating system - History • After programmable general purpose computers were invented, machine languages (consisting of strings of the binary digits 0 and 1 on punched paper tape) were introduced that sped up the programming process (Stern, 1981). https://store.theartofservice.com/the-binary-digit-toolkit.html

18. Central processing unit - Integer range • For example, an 8-bit CPU deals with a range of numbers that can be represented by eight binary digits (each digit having two possible values), that is, 28 or 256 discrete numbers https://store.theartofservice.com/the-binary-digit-toolkit.html

19. Computer data storage - Data organization and representation • Text, numbers, pictures, audio, and nearly any other form of information can be converted into a string of bits, or binary digits, each of which has a value of 1 or 0 https://store.theartofservice.com/the-binary-digit-toolkit.html

20. Integer (computer science) • Integers are commonly represented in a computer as a group of binary digits https://store.theartofservice.com/the-binary-digit-toolkit.html

21. Entropy (information theory) - Entropy as information content • Shannon's definition of entropy, when applied to an information source, can determine the minimum channel capacity required to reliably transmit the source as encoded binary digits (see caveat below in italics). The formula can be derived by calculating the mathematical expectation of the amount of information contained in a digit from the information source. See also Shannon-Hartley theorem. https://store.theartofservice.com/the-binary-digit-toolkit.html

22. Quantum computer • Whereas digital computers require data to be encoded into binary digits (bits), Quantum Computation uses quantum properties to represent data and perform operations on these data https://store.theartofservice.com/the-binary-digit-toolkit.html

23. Digital data - Historical digital systems • More recently invented, a modem modulates an analog "carrier" signal (such as sound) to encode binary electrical digital information, as a series of binary digital sound pulses. A slightly earlier, surprisingly reliable version of the same concept was to bundle a sequence of audio digital "signal" and "no signal" information (i.e. "sound" and "silence") on magnetic cassette tape for use with early home computers. https://store.theartofservice.com/the-binary-digit-toolkit.html

24. Hardware random number generator • A hardware random number generator typically consists of a transducer to convert some aspect of the physical phenomena to an electrical signal, an amplifier and other electronic circuitry to increase the amplitude of the random fluctuations to a macroscopic level, and some type of analog to digital converter to convert the output into a digital number, often a simple binary digit 0 or 1 https://store.theartofservice.com/the-binary-digit-toolkit.html

25. Manchester Small-Scale Experimental Machine - Background • Konrad Zuse's Z3 was the world's first working programmable, fully automatic computer, with binary digital arithmetic logic, but it lacked the conditional branching of a Turing machine https://store.theartofservice.com/the-binary-digit-toolkit.html

26. Manchester Small-Scale Experimental Machine - Williams-Kilburn tube • For use in a binary digital computer, the tube had to be capable of storing either one of two states at each of its memory locations, corresponding to the binary digits (bits) 0 and 1 https://store.theartofservice.com/the-binary-digit-toolkit.html

27. Computer • Inside each 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. https://store.theartofservice.com/the-binary-digit-toolkit.html

28. Data type - Boolean type • The Boolean type represents the values: true and false. Although only two values are possible, they are rarely implemented as a single binary digit for efficiency reasons. Many programming languages do not have an explicit boolean type, instead interpreting (for instance) 0 as false and other values as true. https://store.theartofservice.com/the-binary-digit-toolkit.html

29. Ferranti Mark 1 - History and specifications • The engineers decided to use the simplest mapping between the paper holes and the binary digits they represented, but the mapping between the holes and the physical keyboard was never meant to be a binary mapping https://store.theartofservice.com/the-binary-digit-toolkit.html

30. Ferranti Mark 1 - Mark 1 Star • Instead of the original mapping from holes to binary digits that resulted in the random-looking mapping, the new machines mapped digits to holes in order to produce a much simpler mapping, ø£½0@:$ABCDEFGHIJKLMNOPQRSTUVWXYZ https://store.theartofservice.com/the-binary-digit-toolkit.html

31. Digital electronics - Advantages • An advantage of digital circuits when compared to analog circuits is that signals represented digitally can be transmitted without degradation due to noise. For example, a continuous audio signal transmitted as a sequence of 1s and 0s, can be reconstructed without error, provided the noise picked up in transmission is not enough to prevent identification of the 1s and 0s. An hour of music can be stored on a compact disc using about 6 billion binary digits. https://store.theartofservice.com/the-binary-digit-toolkit.html

32. Digital electronics - Advantages • In a digital system, a more precise representation of a signal can be obtained by using more binary digits to represent it. While this requires more digital circuits to process the signals, each digit is handled by the same kind of hardware. In an analog system, additional resolution requires fundamental improvements in the linearity and noise characteristics of each step of the signal chain. https://store.theartofservice.com/the-binary-digit-toolkit.html

33. Digital electronics - Structure of digital systems • A sequential system is a combinational system with some of the outputs fed back as inputs. This makes the digital machine perform a "sequence" of operations. The simplest sequential system is probably a flip flop, a mechanism that represents a binary digit or "bit". https://store.theartofservice.com/the-binary-digit-toolkit.html

34. Consensus (computer science) - Models of computation • 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}. When the input domain is large relative to the number of processes, for instance an input set of all the natural numbers, it can be shown that consensus is impossible in a synchronous message passing model. https://store.theartofservice.com/the-binary-digit-toolkit.html

35. Binary data • * bit (binary digit) in computer science, https://store.theartofservice.com/the-binary-digit-toolkit.html

36. Computing Machinery and Intelligence - Digital machines • Turing also notes that we need to determine which machines we wish to consider. He points out that a human cloning|clone, while man-made, would not provide a very interesting example. Turing suggested that we should focus on the capabilities of digital machinery—machines which manipulate the binary digits of 1 and 0, rewriting them into memory using simple rules. He gave two reasons. https://store.theartofservice.com/the-binary-digit-toolkit.html

37. Computer & Video Games - Components • Inside each of these parts are thousands to trillions of small electrical network|electrical circuits which can be turned off or on by means of an transistor|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. https://store.theartofservice.com/the-binary-digit-toolkit.html

38. Binary code • A 'binary code' represents Plain text|text or Instruction set|computer processor instructions using the binary number|binary number system's two binary Numerical digit|digits, 0 and 1. A binary code assigns a bit string to each symbol or instruction. For example, a binary String (computer science)|string of eight binary digits (bits) can represent any of 256 possible values and can therefore correspond to a variety of different symbols, letters or instructions. https://store.theartofservice.com/the-binary-digit-toolkit.html

39. Operating systems - History • After programmable general purpose computers were invented, machine languages (consisting of strings of the binary digits 0 and 1 on punched paper tape) were introduced that sped up the programming process (Stern, 1981). https://store.theartofservice.com/the-binary-digit-toolkit.html

40. CPU - Integer range • For example, an 8-bit CPU deals with a range of numbers that can be represented by eight binary digits (each digit having two possible values), that is, 28 or 256 discrete numbers https://store.theartofservice.com/the-binary-digit-toolkit.html

41. Binaries - Structure • Binary files are usually thought of as being a sequence of bytes, which means the binary digits (bits) are grouped in eights https://store.theartofservice.com/the-binary-digit-toolkit.html

42. Digital media • There is a rich history of Numeral system|non-binary digital media, computers, and their rise to prominence over the last couple decades. https://store.theartofservice.com/the-binary-digit-toolkit.html

43. Philosophy of artificial intelligence - Consciousness, minds, mental states, meaning • The difficult philosophical question is this: can a computer program, running on a digital machine that shuffles the binary digits of zero and one, duplicate the ability of the neural correlates of consciousness|neurons to create minds, with mental states (like understanding or perceiving), and ultimately, the experience of consciousness? https://store.theartofservice.com/the-binary-digit-toolkit.html

44. Transmitter - How it works • *A modulator circuit to add the information to be transmitted to the carrier wave produced by the oscillator. This is done by varying some aspect of the carrier wave. The information is provided to the transmitter either in the form of an audio signal, which represents sound, a video signal, or for data in the form of a Binary numeral system|binary Digital data|digital signal. https://store.theartofservice.com/the-binary-digit-toolkit.html

45. Transmitter - How it works • **In an FSK (frequency-shift keying) transmitter, which transmits digital data, the frequency of the carrier is shifted between two frequencies which represent the two binary digits, 0 and 1. https://store.theartofservice.com/the-binary-digit-toolkit.html

46. Quartz clock - Explanation • A 15-bit Binary numeral system|binary Digital electronics|digital counter driven by the frequency will overflow once per second, creating a digital pulse once per second https://store.theartofservice.com/the-binary-digit-toolkit.html

47. Compound word - Recent trends • Although there is no universally agreed-upon guideline regarding the use of compound words in the English language, in recent decades written English has displayed a noticeable trend towards increased use of compounds. Recently, many words have been made by taking syllables of words and compounding them, such as pixel (picture element) and bit (binary digit). This is called a syllabic abbreviation. https://store.theartofservice.com/the-binary-digit-toolkit.html

48. RGB color model - Color depth • The RGB color model is the most common way to encode color in computing, and several different binary numeral system|binary Digital data|digital representations are in use https://store.theartofservice.com/the-binary-digit-toolkit.html

49. Atanasoff–Berry Computer - Design and construction • #Using binary numeral system|binary digits to represent all numbers and data https://store.theartofservice.com/the-binary-digit-toolkit.html

50. Computer storage - Data organization and representation • Text, numbers, pictures, audio, and nearly any other form of information can be converted into a string of bits, or binary digits, each of which has a value of 1 or 0 https://store.theartofservice.com/the-binary-digit-toolkit.html