Booth's multiplication algorithm was invented by Andrew D. Booth in 1951 while studying crystallography at Birkbeck College in London. It improves the speed of computer multiplication by reducing the number of additions or subtractions needed. The algorithm uses a grid with the multiplicand in the top row, the negative multiplicand in the middle row, and the multiplier in the bottom row. It then iteratively shifts and adds or subtracts based on the last two bits of the product to build up the final result in fewer steps than standard addition methods. Several examples are provided to demonstrate how the algorithm works.

1. BOOTH'S MULTIPLICATION ALGORITHM

6. Find 3 × -4, with x = 4 and y = 4: A = 0011 0000 0 S = 1101 0000 0 P = 0000 1100 0 x y 1 A multiplicand zeroes 0 S negative of the multiplicand zeroes 0 P zeroes multiplier 0

8. The last two bits do 00 do nothing 01 P = P + A. Ignore any overflow 10 P = P + S. Ignore any overflow. 11 do nothing