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Explain the Booth’s algorithm in depth with the help off low chart. Give an example for multiplication using Booth’s algorithm. OR Discuss the Booth’s algorithm for 2’s complement number. Also illustrate it with the some example.OR Explain Booth’s multiplication algorithm in detail.

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By Dipali Umre

The algorithm for 2’s complement multiplication is as follows :
Step 1 : Load multiplicand in B, multiplier in Q. For negative numbers, 2’s complement format to be used.
Step 2 : Initialize the down counter CR by the number of bits involved.
Step 3 : Clean locations A (n-bits) and Qn + 1 (1-bit).
Step 4 : Check LS bit of Qn and Qn + 1 jointly. If the pattern is 00 or 11 then go to Step 5. If 10, then A = A – B. If 01, then A = A + B.
Step 5 : Perform arithmetic right-shift with A, Qn and Qn + 1. LS of A goes to MS of Qn and LS of Q goes to Qn + 1. Old content of Qn +1 is discarded.
Step 6 : Decrement CR by one. If CR is not zero then go to Step 4.
Step 7 : Final result (or the product) is available in A (higher part) and Qn(lower part).

Example : Both negative (– 5 × – 4)



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