Question

Use Booth's algorithm to compute (−25×−29).

A) 725
B) 725
C) -725
D) -725

Answer 1

To compute (-25)x(-29) using Booth's algorithm, we convert the negative numbers to their 2's complement form and perform the multiplication steps. therefore correct option is 725

Step-by-step explanation:

To compute (-25)x(-29) using Booth's algorithm, we begin by converting the negative numbers to their 2's complement form. The 2's complement of -25 is 11100111 and the 2's complement of -29 is 11100011. We then perform the multiplication as follows:

1. Write the multiplier (-25) in binary: 11100111
2. Write the multiplicand (-29) in binary: 11100011
3. Write a 0 to the left of the multiplier: 011100111
4. Perform the following steps for each pair of bits:
   1. If the pair of bits is 00 or 11, do nothing.
   2. If the pair of bits is 01, subtract the multiplicand from the accumulator.
   3. If the pair of bits is 10, add the multiplicand to the accumulator.
5. Continue these steps until all pairs of bits are processed.

After performing the multiplication steps, we obtain the result 01111000000110, which is equal to 725 in decimal form.