Three faster multiplication methods are introduced as follows:
- Using Multiple Adders
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Faster multiplications are possible by providing one 32-bit adder for each bit of the multiplier: one input is the multiplicand ANDed with a multiplier bit, and the other is the output of a prior adder. This approach is to connect the outputs of adders on the right to the inputs of adders on the left, making a stack of adders 32 high. The hardware has the following features:
- 32-bit adder for each bit of the multiplier:
- 31 adders are needed for a 32-bit multiplier.
- AND multiplicand with each bit of multiplier.
- Product = accumulated shifted sum.
- Each adder produces a 33-bit output:
- Most significant bit is a carry bit.
- Least significant bit is a product bit.
- Upper 32 bits go to next adder.
- Array multiplier can be optimized:
- Carry save adders reduce delays.
- Pipelining further improves the speed.
The symbol is commonly used to represent an ALU or an adder. - 32-bit adder for each bit of the multiplier: