Given positive, integer N, what does this algorithm produce?

let S and D = N
repeat 
    let D = ⌊D/2⌋
    subtract D from S
until D=0
produce S as the result

Note: ⌊x⌋ represents the integer part of x.

For non-programmers: start with a positive, integer number (say, 19). Divide it by 2, discarding remainders, until you get to 0. (In this case, you'd get 9, 4, 2, and 1.) Sum all the quotients. (9+4+2+1=16.) Subtract the sum from the original number. (19-16=3.) What's the result?

in addition to finding the number of one in a binary number reprerentation, this algoritm can be used as a binary gereator (and often is)working from right to left divide interger by two, if no remainder bit is 0 if remainder exists bit is 1 repeat.

Posted by sjh182 on 2005-01-20 06:53:59