Multiplication (2025-26 Q1f)

Computer Organization and Architecture2025-262 marksNumericalMultiplication

Explain signed number multiplication using Booth's Algorithm. Multiply A x B where A= -5 and B=3 using Booth's Algorithm.

Booth's algorithm multiplies signed 2's complement numbers. For each bit pair $Q_0Q_{-1}$ : $10$ subtracts $M$ , $01$ adds $M$ , otherwise nothing. Then it shifts right (ASR).

Here $M = -5 = 1011$ , $-M = 0101$ and $Q = 3 = 0011$ .

Cycle	Action	A	Q	Q-1
1	A - M	0010	1001	1
2	shift	0001	0100	1
3	A + M	1110	0010	0
4	shift	1111	0001	0

$AQ = 11110001 = -15$ . Therefore $(-5) \times 3 = -15$ .

Booth's algorithm multiplies signed 2's complement numbers. For each bit pair $Q_0Q_{-1}$: $10$ subtracts $M$, $01$ adds $M$, otherwise nothing. Then it shifts right (ASR).

Here $M = -5 = 1011$, $-M = 0101$ and $Q = 3 = 0011$.

Cycle	Action	A	Q	Q-1
1	A - M	0010	1001	1
2	shift	0001	0100	1
3	A + M	1110	0010	0
4	shift	1111	0001	0

$AQ = 11110001 = -15$. Therefore $(-5) \times 3 = -15$.

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