# a) Show that this algorithm determines the number of 1 ## Problem 10E Chapter 3.3

Discrete Mathematics and Its Applications | 7th Edition

• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants Discrete Mathematics and Its Applications | 7th Edition

4 5 0 262 Reviews
12
0
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

##### ISBN: 9780073383095

×
Get Full Access to Discrete Mathematics And Its Applications - 7th Edition - Chapter 3.3 - Problem 10e

Get Full Access to Discrete Mathematics And Its Applications - 7th Edition - Chapter 3.3 - Problem 10e

I don't want to reset my password

Need help? Contact support

Need an Account? Is not associated with an account
We're here to help