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The modern binary number system, the basis for binary code, is an invention by Gottfried Leibniz in 1689 and appears in his article Explication de l'Arithmétique Binaire (English: Explanation of the Binary Arithmetic) which uses only the characters 1 and 0, and some remarks on its usefulness. Leibniz's system uses 0 and 1, like the modern ...
There are tricks for implementing packed BCD and zoned decimal add–or–subtract operations using short but difficult to understand sequences of word-parallel logic and binary arithmetic operations. [49] For example, the following code (written in C) computes an unsigned 8-digit packed BCD addition using 32-bit binary operations:
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 ...
A common usage of a barrel shifter is in the hardware implementation of floating-point arithmetic. For a floating-point add or subtract operation, the significands of the two numbers must be aligned, which requires shifting the smaller number to the right, increasing its exponent, until it matches the exponent of the larger number. This is done ...
A diagram showing how manipulating the least significant bits of a color can have a very subtle and generally unnoticeable effect on the color. In this diagram, green is represented by its RGB value, both in decimal and in binary. The red box surrounding the last two bits illustrates the least significant bits changed in the binary representation.
A bitstream (or bit stream), also known as binary sequence, is a sequence of bits. A bytestream is a sequence of bytes . Typically, each byte is an 8-bit quantity , and so the term octet stream is sometimes used interchangeably.
The RFC 1982 algorithm specifies that, for N-bit sequence numbers, there are 2 N−1 − 1 values considered "greater than" and 2 N−1 − 1 considered "less than". Comparison against the remaining value (exactly 2 N−1-distant) is deemed to be "undefined". Most modern hardware implements signed two's complement binary
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 RAM or CPU registers, numbers are represented only as sequences of bits, without extra symbols.