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# a) Show that this algorithm determines the number of 1

ISBN: 9780073383095 37

## Solution for problem 10E Chapter 3.3

Discrete Mathematics and Its Applications | 7th Edition

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Problem 10E

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 bi Is to t he 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 pan (a)?

Step-by-Step Solution:

Solution:Step 1</p>

In this problem we need to show that the given algorithm counts the number of 1’s in a bit string. We also need to find the number of AND operations are computed to find the number of 1 bits in a bit string using the given algorithm.

Step 2 of 2

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