Canonical signed digit

In computing canonical-signed-digit (CSD) is a special manner for encoding a value in a signed-digit representation, which itself is non-unique representation and allows one number to be represented in many ways.  Probability of digit being zero is close to 66% (vs. 50% in two's complement encoding) and leads to efficient implementations of add/subtract networks (e.g. multiplication by a constant) in hardwired digital signal processing.

The representation uses a sequence of one or more of the symbols, -1, 0, +1 (alternatively -, 0 or +) with each position possibly representing the addition or subtraction of a power of 2.  For instance 23 is represented as +0-00-, which expands to  or

Implementation
CSD is obtained by transforming every sequence of zero followed by ones (011...1) into + followed by zeros and the least significant bit by - (+0....0-).

As an example: the number 7 has a two's complement representation 0111 

into +00-

References

External links
 Introduction to Canonical Signed Digit Representation
 

Category:Computing terminology