What is a canonical signed digit?

Question

What is a canonical signed digit (CSD) and how does one convert a binary number to a CSD and a CSD back to a binary number? How do you know if a digit of a CSD should be canonically chosen to be +, -, or 0?

Answer 1

Signed-digit binary uses three symbols in each power-of-two position: -1, 0, 1. The value represented is the sum of the positional coefficients times the corresponding power of 2, just like binary, the difference being that some of the coefficients may be -1. A number can have multiple distinct representations in this system.

Canonical signed digit representation is the same, but subject to the constraint that no two consecutive digits are non-0. It works out that each number has a unique representation in CSD.

See slides 31 onwards in Parhi's Bit Level Arithmetic for more, including a binary to CSD conversion algorithm.