ECE-C451 Computer Arithmetic Fall term 2010

Homework #7 Solution

1. Given A = (E5)16 and B = (F2)16 Perform the multiplication A x B using the following algorithms:

a. Shiftleft A. B   First version

b. Shiftleft A. Shiftright B   Second version

c. Booth’s Algorithm Compare these three operations and comment.

2. You are given the following two numbers to multiply (A x B): A = 101110101111011101110 B = 011111000111101100110

How many operations will this take using:

a. Booth’s Algorithm b. Modified Booth’s Algorithm

3. Try to implement the Modified Booth’s Algorithm in a circuit. Estimate the space and time complexity of your circuit. Steps to follow:

a. Review the table on page #4 of Handout #4, which compares the complexity of the various algorithms for multiplication. The last row of the table is for the Modified Booth’s Algorithm. Describe how this algorithm differs from Booth’s Algorithm.

b. Consider your answer from a, instead of 2 bits, you must look at 3 bits in the divisor.