Booth’s Algorithm for Multiplication of Binary Numbers
Shift-and-add multiplication
Shift-and-add multiplication is similar to the multiplication performed by paper and pencil. This
method adds the multiplicand X to itself Y times, where Y denotes the multiplier. In the case
of binary multiplication, since the digits are 0 and 1, each step of the multiplication is simple. If
the multiplier digit is 1, a copy of the multiplicand (1 × multiplicand) is placed in the proper
positions; if the multiplier digit is 0, a number of 0 digits (0 × multiplicand) are placed in the
proper positions.
The multiplier circuit, which implements the shift-and-add multiplication method for two n-bit
numbers. The Circuit Diagram for Multiplication of n-bit numbers (Product 2n bits?)
The 2n-bit product register (A) is initialized to 0. Since the basic algorithm shifts the
multiplicand register (B) left one position each step to align the multiplicand with the sum being
accumulated in the product register, we use a 2n-bit multiplicand register with the multiplicand
placed in the right half of the register and with 0 in the left half. The Multiplier is 4 bits long so
n = 4.
