Editing Signed number representations (section)

== {{anchor|Excess-128|Excess-K}}Offset binary ==
{{Main|Offset binary}}

{|class="wikitable" style="float:right; width: 20em; margin-left: 1em; text-align:center"
|+ Eight-bit excess-128
|-
!Binary value
!Excess-128 interpretation
!Unsigned interpretation
|-
| 00000000 || −128 || 0
|-
| 00000001 || −127 || 1
|-
| ⋮ || ⋮ || ⋮
|-
| 01111111 || −1 || 127
|-
| 10000000 || 0 || 128
|-
| 10000001 || 1 || 129
|-
| ⋮ || ⋮ || ⋮
|-
| 11111111 || 127 || 255
|-
|}

In the ''offset binary'' representation, also called ''excess-<var>K</var>'' or ''biased'', a signed number is represented by the bit pattern corresponding to the unsigned number plus <var>K</var>, with <var>K</var> being the ''biasing value'' or ''offset''. Thus 0 is represented by <var>K</var>, and −<var>K</var> is represented by an all-zero bit pattern. This can be seen as a slight modification and generalization of the aforementioned two's-complement, which is virtually the {{nobr|excess-(2<sup><var>N</var>−1</sup>)}} representation with [[negated]] [[most significant bit]].

Biased representations are now primarily used for the exponent of [[floating-point]] numbers. The [[IEEE 754|IEEE 754 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]].