Wallace Tree Multiplier
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Author: Eric Manwill
Project access type: Public

An example of unsigned binary multiplication in hardware, using a Wallace tree.
The Wallace tree has three steps:
  1. Multiply each of the bits of the multiplicand by each of the bits of the operator. This is the grid of AND gates seen at the top of the circuit. For an x-bit multiplicand and y-bit multiplier, this step creates y partial products ranging from x bits to (x+y-1) bits in length.
  2. Reduce the number of partial products from step 1 down to two by successive layers of full and half adders. In this circuit, you can see four layers of full and half adders performing this reduction. Note that the carry-out bit (co) of each addition is passed down to the next reduction stage rather than to the next adder leftward in the same stage.
  3. Perform a final stage of addition on the remaining two partial products using a conventional adder. This is the final layer of full adders at the bottom of this circuit.

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