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34 votes
34 votes

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?

  1. $6$
  2. $8$
  3. $10$
  4. $12$
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5 Answers

34 votes
34 votes

Answer is B.

Append 0 the end of multiplier : $0111$ $0111$ $1011$ $1101$ 0

Now,Paired bits from right end as $00$-(0), $01$-(+1), $10$(-1) and $11$-(0)

note:- pairs are overlapped.

Count +1=4 (additions required)

Count -1=4 (subtractions required)

So, total 8 pair hence addition/subtraction required = $8$.

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19 votes
19 votes

Answer : 8

If you want to find out How many additions/Subtractions are required for the multiplication using Booth's algorithm. then Rules are like this

Take multiplicand and multiplier like they are given in the question :

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

Now find out the 01 and 10 pairs combinedly means see both Multiplicand and Multiplier simultaneously first pair is 00 then 11 ,01 ,11 , 10  01  11  01  11  10  11  01  11  11  10  01 

why i asked you to do this because this is the rule a/c to Booth's algorithm. to find out no of additions/Subtractions it also says don't do anything if you got 11 or 00 .

18 votes
18 votes
it's 8 (4 addition and 4 subtractions)
11 votes
11 votes

A faster way to answer this is to see how many groups of 1's are present in multiplier. (This only works for positive numbers.)

Multiplier = 0111011110111101

Number of  groups of 1's = 4

Number of additions = Number of subtractions = Number of groups of 1's = 4

or Number of additions/ subtractions = 4 *2 = 8

Answer:

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