Chapter 3.3, Problem 10E

1. Show that this algorithm determines the number of 1 bits in the bit string S:

procedurebit count(S: bit string)

count:= 0

while $S\ne 0$

count:=count+ 1

   $S\wedge \left(S-1\right)$

returncount{countis the number of 1s inS}

Here $S-1$is the bit string obtained by changing the rightmost 1 bit ofSto a 0 and all the 0 bits to the right of this to 1s. [Recall that $S\wedge \left(S-1\right)$is the bitwise AND ofSand $S-1$]

1. How many bitwiseANDoperations are needed to find the number of 1 bits in a stringSusing the algorithm in part (a)?