Booth’s Algorithm is an efficient method for multiplying signed binary numbers in two’s complement form. It reduces the number of additions/subtractions by encoding patterns in the multiplier, making it faster than standard binary multiplication, especially in hardware implementations like ALUs and DSPs.

Core Idea: Inspect the last two bits of the multiplier (Qn and Qn+1) to decide whether to add, subtract, or do nothing with the multiplicand, followed by an Arithmetic Shift Right (ASR). This continues until all bits are processed.

Flowchart Steps:

1. Initialization AC = 0 (Accumulator) QR = Multiplier BR = Multiplicand Qn+1 = 0 (extra bit) SC = n (number of bits in multiplier)

2. Check Bit Pair (Qn, Qn+1) 10 → Subtract BR from AC 01 → Add BR to AC 00 or 11 → No change

3. Arithmetic Shift Right Shift [AC, QR, Qn+1] right by 1 bit (sign bit preserved in AC).

4. Decrement SC Repeat steps 2–4 until SC = 0.

5. Result Final product is in [AC, QR].

Example (n=4, Multiplying 5 × -3):