Non-adjacent form

The non-adjacent form (NAF) of a number is a unique signed-digit representation, in which non-zero values cannot be adjacent.

NAF assures a unique representation of an integer, but the main benefit of it is that the Hamming weight of the value will be minimal.

For regular binary representations of values, half of all bits will be non-zero, on average, but with NAF this drops to only one-third of all digits.

This leads to efficient implementations of add/subtract networks (e.g. multiplication by a constant) in hardwired digital signal processing.

The properties of NAF make it useful in various algorithms, especially some in cryptography; e.g., for reducing the number of multiplications needed for performing an exponentiation.