Given the following values in the indicated bases: R1 (7460)s and R2-(A8D)1 a- C

Question

Given the following values in the indicated bases: R1 (7460)s and R2-(A8D)1 a- Convert R1 and R2 into binary values (the sign bit is Included in the above values where negative numbers are already in 2's complement). b Select the most economical multiplier from R1 and R2 for Booth's algorthm c Convert the multiplicand into 2's complement and insert it into (-M d- Use Booth's algorithm to multiply the multiplier by the multiplicand and insert all intermediate values in the provided space below Ri R2 -M Multiplicand Multiplier

Explanation / Answer

GIVEN VALUES-

R1= ( 7460 )8  AND R2= ( A8D )16

a) R1= ( 7460 )8 = (1111 0011 0000)2

R2= ( A8D )16 = (1010 1000 1101)2

b) The most ECONOMICAL MULTIPLIER among R1 and R2 is = R1 i.e 1111 0011 0000

because while taking R1 as the multiplier, the majority of the time processor just have to do shift only task rather than addition or subtraction.

c) The multiplicand is = 1010 1000 1101

2's complement of multiplicand= 0101 0111 0011

-M = 0 1 0 1 0 1 1 1 0 0 1 1

d)

FINAL RESULT IS = 0000 0100 0110 1101 0111 0000 = (290160)10

(multiplicand) = 1 0 1 0 1 0 0 0 1 1 0 1 = (-1395)10 (multiplier) = 1 1 1 1 0 0 1 1 0 0 0 0 = (-208)10 (re-coded 0 0 0 -1 0 1 0 -1 0 0 0 0 multiplier)
Shift Only 0 0 0 0 0 0 0 0 0 0 0 0 0 Shift Only 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Shift Only 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Shift Only 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Add (-A) + 0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 1 0 1 1 1 0 0 1 1 0 0 0 0 Shift only 0 0 1 0 1 0 1 1 1 0 0 1 1 0 0 0 0 Shift Only 0 0 0 1 0 1 0 1 1 1 0 0 1 1 0 0 0 0 Add (A) + 1 0 1 0 1 0 0 0 1 1 0 1 1 0 1 1 1 1 1 0 1 0 0 1 1 1 0 0 0 0 Shift 1 1 0 1 1 1 1 1 0 1 0 0 1 1 1 0 0 0 0 Shift Only 1 1 1 0 1 1 1 1 1 0 1 0 0 1 1 1 0 0 0 0 Add (-A) + 0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 1 0 1 1 1 0 0 0 0 Shift 0 0 1 0 0 0 1 1 0 1 1 0 1 0 1 1 1 0 0 0 0 Shift Only 0 0 0 1 0 0 0 1 1 0 1 1 0 1 0 1 1 1 0 0 0 0 Shift Only 0 0 0 0 1 0 0 0 1 1 0 1 1 0 1 0 1 1 1 0 0 0 0 Shift Only 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 1 0 1 1 1 0 0 0 0 = (290160)10

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