x 7 c 7 x 0 A : a 7 a 0 y 7 y 0 s 7 s 0 0 x 8 x 7 c 8 P = 3 A : P 9 x 0 y 8 y 7 y 0 s 8 s 0 P 8 P 0 (a) Naive approach A : a 7 0 x 8 c 8 P = 3 A : P 9 x 1 x 0 a 0 0 y 8 y 7 y 0 s 8 s 0 P 8 P 0 (b) Efficient design Figure 5. 7 Circuit that multiplies an 8 -bit unsigned number by 3
Multiplicand M Multiplier Q (14) (11) 1110 ´ 1011 1110 0000 1110 Product P (154) 10011010 (a) Multiplication by hand Multiplicand M Multiplier Q (11) (14) Partial product 0 Partial product 1 Partial product 2 Product P (154) 1110 ´ 1011 1110 + 1110 10101 + 0000 01010 + 1110 10011010 (b) Multiplication for implementation in hardware Figure 5. 32 Multiplication of unsigned numbers