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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?
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
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The two numbers given below are multiplied using the Booth's algor...
Booth's algorithm is used for multiplying two binary numbers. It reduces the number of operations required for multiplication by using a technique of shifting and adding. The steps involved in the Booth's algorithm are as follows:
1. Initialize the product register to 0 and the multiplier to the given binary number.
2. Add a 0 bit to the right end of the product register.
3. Repeat the following steps n times, where n is the number of bits in the multiplier:
a. If the last two bits of the product register are 01, subtract the multiplicand from the product register.
b. If the last two bits of the product register are 10, add the multiplicand to the product register.
c. Shift the product register right by 1 bit.
d. Shift the multiplier right by 1 bit.
4. Remove the extra 0 bit from the product register to get the final result.
In the given problem, the multiplicand is 0101101011101110 and the multiplier is 0111011110111101. Therefore, the number of bits in the multiplier is 16.
To determine the number of additions/subtractions required for the multiplication, we need to count the number of times steps a and b are performed in the algorithm.
In this case, step a is performed 4 times and step b is performed 4 times. Therefore, the total number of additions/subtractions required is 4+4=8.
Hence, the correct option is B.
1. Initialize the product register to 0 and the multiplier to the given binary number.
2. Add a 0 bit to the right end of the product register.
3. Repeat the following steps n times, where n is the number of bits in the multiplier:
a. If the last two bits of the product register are 01, subtract the multiplicand from the product register.
b. If the last two bits of the product register are 10, add the multiplicand to the product register.
c. Shift the product register right by 1 bit.
d. Shift the multiplier right by 1 bit.
4. Remove the extra 0 bit from the product register to get the final result.
In the given problem, the multiplicand is 0101101011101110 and the multiplier is 0111011110111101. Therefore, the number of bits in the multiplier is 16.
To determine the number of additions/subtractions required for the multiplication, we need to count the number of times steps a and b are performed in the algorithm.
In this case, step a is performed 4 times and step b is performed 4 times. Therefore, the total number of additions/subtractions required is 4+4=8.
Hence, the correct option is B.
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