Answered: Show that this algorithm determines the…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

a) Show that this algorithm determines the number of 1
bits in the bit string S:
procedure bit count(S: bit string)
count := 0
while S ≠ 0
count := count + 1
S := S ∧ (S − 1)
return count {count is the number of 1s in S}
Here S − 1 is the bit string obtained by changing the
rightmost 1 bit of S to a 0 and all the 0 bits to the
right of this to 1s. [Recall that S ∧ (S − 1) is the bitwise AND of S and S − 1.]

b) How many bitwise AND operations are needed to find
the number of 1 bits in a string S using the algorithm
in part (a)?

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