Talk:Non-adjacent form

The paragraph on alternating signs is not correct. Just consider the binary representation of decimal 9, being 1001, which is its unique NAF form.

It is however correct that the Booth Algorithm determines a signed digit representation where the signs of the non-zero digits alternate.

BUT the Booth algorithm does not generate a NAF representation! Take as an example a binary string with an isolated 1, say ...$00100$..., which by the Booth Algorithm converts into ...$01{\bar {1}}$...

The original algorithm for converting a binary number into its equivalent and unique NAF form was given by Reitwiesner in 1960, but normally it is described by the following right-to-left algorithm:

Input: $b_{n-1}\cdots b_{1}b_{0}$ in 2's complement
Output: $e_{n}e_{n-1}\cdots e_{1}e_{0}$
$c_{0}:=0;\ b_{n+1}:=b_{n}:=b_{n-1};$
for $i:=0$ to $n$ do

 $c_{i+1}:=\lfloor (c_{i}+b_{i}+b_{i+1})/2\rfloor ;$

 $e_{i}:=c_{i}+b_{i}-2c_{i+1};$

end

Encoding the NAF of an m-bit number using m+1 bits

The article currently states that "[b]cause every non-zero value has to be adjacent to two 0's, the NAF representation can be implemented such that it only takes a maximum of m + 1 bits for a value that would normally be represented in binary with m bits." Can someone provide more details on this "implementation"? 188.169.229.30 (talk) 19:39, 27 April 2013 (UTC)