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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]
The bfloat16 binary floating-point exponent is encoded using an offset-binary representation, with the zero offset being 127; also known as exponent bias in the IEEE 754 standard. E min = 01 H −7F H = −126; E max = FE H −7F H = 127; Exponent bias = 7F H = 127
The half-precision binary floating-point exponent is encoded using an offset-binary representation, with the zero offset being 15; also known as exponent bias in the IEEE 754 standard. [9] E min = 00001 2 − 01111 2 = −14; E max = 11110 2 − 01111 2 = 15; Exponent bias = 01111 2 = 15
The double-precision binary floating-point exponent is encoded using an offset-binary representation, with the zero offset being 1023; also known as exponent bias in the IEEE 754 standard. Examples of such representations would be:
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The octuple-precision binary floating-point exponent is encoded using an offset binary representation, with the zero offset being 262143; also known as exponent bias in the IEEE 754 standard. E min = −262142