Binary Multiplication

Binary multiplication is is explained using two approaches

1. Using the simple binary multiplication
2. Using the Binary 2’s complement Booth’s Multiplication Algorithm

first we explain using the first approach

Simple binary multiplication

Fig: Binary multiplication Algo

Example-1: Multiply 22 and 21 using binary multiplication algorithm explain figure above 

Multiplicand Register B = 22 = 10110

Multiplier Register Q = 21= 10101

	Step	Qn	Operation	Carry (E)	Acc (A)	Multiplier (Q)	Count
	initialize	x	x	0	00000	10101	5
	1,	1,	A=A+B		00000 10110 ——— 10110
			Shr EAQ	0	01011	01010	4
	2	0	Shr EAQ	0	00101	10101	3
	3	1	Add	0	00101 10110 ——– 11011
			Shr EAQ	0	01101	11010	2
	4	0	Shr EAQ	0	00110	11101	1
	5	1	Add	0	00110 10110 ——– 11100
			Shr EAQ	0	01110	01110	0
	ANSWER		22 x 21 = 462 = 00111001110

Example-2 : Multiply 30 and 26 using Binary Multiplication Algorithm

Multiplicand Register B = 30 = 11110

Multiplier Register Q = 26= 11010

	Step	Qn	Operation	Carry (E)	Acc (A)	Multiplier (Q)	Count
	initialize	x	x	0	00000	11010	5
	1,	0	Shr EAQ	0	00000	01101	4
	2	1	Add A, B	0	00000 11110 ——– 11110
			Shr EAQ	0	01111	00110	3
	3	0	Shr EAQ	0	00111	10011	2
	4	1	Add	1	00111 11110 ——– 00101	10011
			Shr EAQ	0	10010	11001	1
	5	1	Add	1	10010 11110 ——— 10000
		0	Shr EAQ	0	11000	01100	0
	ANSWER		30×26 = 780 = 01100001100

2’sComplement Multiplication Booth’s Algorithm

Example multiply -12 x -20 using Booth’s Algorithm

Let

multiplicand = -20 ; Reg B(- 20) =101100

2’s Complement B’+1 = (+20) = 010100

Multipler Reg Q = -12 = 10100

-20 x -12 = 240

Fig: Booth’s Algo for 2’s compliment multiplication

Booth’s Algorith	Step	Qn	Qn+1	Operation	Acc	Q = -12	Qn+1	Count
	initialize		0	Initialize Acc, Q, B, Qn+1	000000	10100	0(initial value)	5
	1	0	0	Arithmetic shift right (AQQn+1)	000000	01010	0	4
	2	0	0	Arithmetic shift right (AQQn+1)	000000	00101	0	3
	3	1	0	A-B=A+B’+1	000000 010100 ———- 010100
				Arithmetic shift right (AQQn+1)	001010	00010	1	2
	4	0	1	A+B	001010 101100 ———- 110110
				Arithmetic shift right (AQQn+1)	111011	00001	0	1
	5	1	0	A-B	111011 010100 ———- 001111
				Arithmetic shift right (AQQn+1)	000111	10000	1	0 stop
	ANSWER			-20 x -12 = +240 = 00011110000

Binary Division Algorithm

Example: