Signed-digit representation
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Signed-digit representation of numbers indicates that values can be prefixed with a − (minus) sign to indicate that they are negative.
Signed-digit representation can be used in low-level software and hardware to accomplish fast high speed addition of integers because it can eliminate carries. In the binary numeral system one special case of signed-digit representation is the non-adjacent form which can offer speed benefits with minimal space overhead.
Note that signed-digit representation is not necessarily unique. For instance:
- (0 1 1 1) = 4 + 2 + 1 = 7
- (1 0 −1 1) = 8 − 2 + 1 = 7
- (1 −1 1 1) = 8 − 4 + 2 + 1 = 7
- (1 0 0 −1) = 8 − 1 = 7
The non-adjacent form does guarantee a unique representation for every value.
