Excess-K
Binary value | Excess-127 interpretation | Unsigned interpretation |
---|---|---|
00000000 | −127 | 0 |
00000001 | −126 | 1 |
⋮ | ⋮ | ⋮ |
01111111 | 0 | 127 |
10000000 | 1 | 128 |
⋮ | ⋮ | ⋮ |
11111111 | +128 | 255 |
Excess-K, also called offset binary or biased representation, uses a pre-specified number K as a biasing value. A value is represented by the unsigned number which is K greater than the intended value. Thus 0 is represented by K, and −K is represented by the all-zeros bit pattern. This can be seen as a slight modification and generalization of the aforementioned two's-complement, which is virtually the excess-2N−1 representation with negated most significant bit.
Biased representations are now primarily used for the exponent of floating-point numbers. The IEEE floating-point standard defines the exponent field of a single-precision (32-bit) number as an 8-bit excess-127 field. The double-precision (64-bit) exponent field is an 11-bit excess-1023 field; see exponent bias. It also had use for binary coded decimal numbers as excess-3.
Read more about this topic: Signed Number Representations