Question

Explain Booth multiplication algoauthm. Solve the
following using Booth's multiplication algouthin's
Multiplicand=01111 (M)
Multiplier=10011 (Q)​

Answer 1

Answer:

Booth algorithm gives a procedure for multiplying binary integers in signed 2’s complement representation in efficient way, i.e., less number of additions/subtractions required. It operates on the fact that strings of 0’s in the multiplier require no addition but just shifting and a string of 1’s in the multiplier from bit weight 2^k to weight 2^m can be treated as 2^(k+1 ) to 2^m.

Explanation:

The multiplicand is added to the partial product upon encountering the first 0 (provided that there was a previous ‘1’) in a string of 0’s in the multiplier.

The partial product does not change when the multiplier bit is identical to the previous multiplier bit.

Hardware Implementation of Booths Algorithm – The hardware implementation of the booth algorithm requires the register configuration shown in the figure below.

AC and the appended bit Qn+1 are initially cleared to 0 and the sequence SC is set to a number n equal to the number of bits in the multiplier. The two bits of the multiplier in Qn and Qn+1are inspected. If the two bits are equal to 10, it means that the first 1 in a string has been encountered. This requires subtraction of the multiplicand from the partial product in AC. If the 2 bits are equal to 01, it means that the first 0 in a string of 0’s has been encountered. This requires the addition of the multiplicand to the partial product in AC.