Question

Given the following values in the indicated bases: R1=(7460)_8, R2=(A8D)_16, and R3=(000)_16. a- Convert R1, R2 and R3 into binary values (the sign bit is included in the above values where negative numbers are already in 2's complement) b- Use sign extension rules to double the size of each register c- Select the most economical multiplier from R1 and R2 for Booth's algorithm d- Use Booth's algorithm to multiply multiplier by multiplicand indicating all intermediate values R1 R2

Answer 1

a)The Binary values are:

R1 : 111100110000

R2 : 101010001101

R3 : 000011010000

b) The binary values after applying sign extension are:

R1 : 111111111111111100110000

R2 : 111111111111101010001101

R3 : 000000000000000011010000

c)R1 is the economic multiplier for Booth's Algorithm as it has continuos bits of 0s and 1s leading to shift.