GATE IT 2008 | Question: 42

Question

The two numbers given below are multiplied using the Booth's algorithm.

Multiplicand :                            $0101$ $1010$ $1110$ $1110$
Multiplier:                                  $0111$ $0111$ $1011$ $1101$

How many additions/Subtractions are required for the multiplication of the above two numbers?

• A. $6$
• B. $8$
• C. $10$
• D. $12$

Comments

Answer in go pdf is wrong for this one ..Please correct it in next edition

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if question is about no. of additions/Subtractions  required for the multiplication of the given two numbers

then,finding booths coding of multiplier is enough.

0111 0111 1011 1101

+1 0 0 -1  +1 0 0 0  -1 + 1 0 0  0 -1 +1 -1

that is 8 (4 additions + 4 subtractions)

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For each block of consecutive 1’s we need one addition and one subraction

Answer 1

Number is: 0111011110111101

For making the Booth's code we add 0 temporarily in the right most side and then select each bit from left to right and note down the final result.

 

     

Position	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17
Value with temporary 0 at right side	0	1	1	1	0	1	1	1	1	0	1	1	1	1	0	1	0
Booth recoding	0	1	0	0	-1	1	0	0	0	-1	1	0	0	0	-1	1	-1

Total addition = 4

Total Subtraction =4

Total addition and subtraction =8

Comments

sir why you consider only multilpier why not multiplicand for booth recoding