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Offset binary, [1] also referred to as excess-K, [1] excess-N, excess-e, [2] [3] excess code or biased representation, is a method for signed number representation where a signed number n is represented by the bit pattern corresponding to the unsigned number n+K, K being the biasing value or offset.
In the offset binary representation, also called excess-K or biased, a signed number is represented by the bit pattern corresponding to the unsigned number plus K, with K being the biasing value or offset. Thus 0 is represented by K, and −K is represented by an all-zero bit pattern.
In IEEE 754 floating-point numbers, the exponent is biased in the engineering sense of the word – the value stored is offset from the actual value by the exponent bias, also called a biased exponent. [1]
In computing, half precision (sometimes called FP16 or float16) is a binary floating-point computer number format that occupies 16 bits (two bytes in modern computers) in computer memory. It is intended for storage of floating-point values in applications where higher precision is not essential, in particular image processing and neural networks .
Double-precision binary floating-point is a commonly used format on PCs, due to its wider range over single-precision floating point, in spite of its performance and bandwidth cost. It is commonly known simply as double. The IEEE 754 standard specifies a binary64 as having: Sign bit: 1 bit; Exponent: 11 bits
In this (original) meaning of offset, only the basic address unit, usually the 8-bit byte, is used to specify the offset's size. In this context an offset is sometimes called a relative address. In IBM System/360 instructions, a 12-bit offset embedded within certain instructions provided a range of between 0 and 4096 bytes. For example, within ...
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 ...
The quadruple-precision binary floating-point exponent is encoded using an offset binary representation, with the zero offset being 16383; this is also known as exponent bias in the IEEE 754 standard. E min = 0001 16 − 3FFF 16 = −16382; E max = 7FFE 16 − 3FFF 16 = 16383; Exponent bias = 3FFF 16 = 16383