9.6. Multiplier Design
First some basics of multiplication:
There are two methods to implement the above multiplication operation.
Multiplier Design using 2-operand Adders
Multiplier Design using Multiple-Operand Adder
Am ... A 2 A 1 A 0 Multiplicand (m bits)
Bn ... B 2 B 1 B 0 Multiplicand (n bits)
_____________________X ... X X X X Partial Product 0
X ... X X X X Partial Product 1
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X ... X X X X Partial Product n
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R(m+n) ... R 2 R 1 R 0 Result (m+n bits)Truth-table for a 2-bit by 2-bit multiply
A1 A0 B1 B0 R3 R2 R1 R0
0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0
0 0 1 0 0 0 0 0
0 0 1 1 0 0 0 0
0 1 0 0 0 0 0 0
0 1 0 1 0 0 0 1
0 1 1 0 0 0 1 0
0 1 1 1 0 0 1 1
1 0 0 0 0 0 0 0
1 0 0 1 0 0 1 0
1 0 1 0 0 1 0 0
1 0 1 1 0 1 1 0
1 1 0 0 0 0 0 0
1 1 0 1 0 0 1 1
1 1 1 0 0 1 1 0
1 1 1 1 1 0 0 1