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Binary zero, represented by the forward slash, was the most common character in programs and data, leading to sequences written as "/////". One early user suggested that Turing's choice of a forward slash was a subconscious choice on his part, a representation of rain seen through a dirty window, reflecting Manchester's "famously dismal" weather.
A binary encoding is inherently less efficient for conversions to or from decimal-encoded data, such as strings (ASCII, Unicode, etc.) and BCD. A binary encoding is therefore best chosen only when the data are binary rather than decimal. IBM has published some unverified performance data. [2]
If ten bits are used to represent the value "11 1111 0001" (decimal negative 15) using two's complement, and this is sign extended to 16 bits, the new representation is "1111 1111 1111 0001". Thus, by padding the left side with ones, the negative sign and the value of the original number are maintained.
The base-2 numeral system is a positional notation with a radix of 2.Each digit is referred to as a bit, or binary digit.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, as a preferred system of use, over various other human techniques of communication, because ...
Two's complement is the most common method of representing signed (positive, negative, and zero) integers on computers, [1] and more generally, fixed point binary values. Two's complement uses the binary digit with the greatest value as the sign to indicate whether the binary number is positive or negative; when the most significant bit is 1 the number is signed as negative and when the most ...
The formal definition of an arithmetic shift, from Federal Standard 1037C is that it is: . A shift, applied to the representation of a number in a fixed radix numeration system and in a fixed-point representation system, and in which only the characters representing the fixed-point part of the number are moved.
In base 2, 10110 (22 in decimal) has been proven to be a Lychrel number, since after 4 steps it reaches 10110100, after 8 steps it reaches 1011101000, after 12 steps it reaches 101111010000, and in general after 4n steps it reaches a number consisting of 10, followed by n + 1 ones, followed by 01, followed by n + 1 zeros. This number obviously ...
When converting from binary to octal every 3 bits relate to one and only one octal digit. Hexadecimal, decimal, octal, and a wide variety of other bases have been used for binary-to-text encoding, implementations of arbitrary-precision arithmetic, and other applications. For a list of bases and their applications, see list of numeral systems.