Implementing Large Multiplier Using Smaller ones

By DR. SHIRSHENDU ROY / 18th June 2019 / Uncategorized

Like Booth’s multiplication algorithm another method reduction of partial products is implementing higher multipliers by smaller ones. The larger multiplier blocks can be realized using smaller multiplier blocks. A $2n\times 2n$ multiplier can be realized using four $n\times n$ multiplier blocks. This is based on the following equation

$A.X = (A_H.2^n + A_L).(X_H.2^n + X_L) =A_H.X_H.2^{2n}+(A_H.X_L+A_L.X_H).2^n + (A_L.X_L)$

where $A_H$ is the most significant halve of A, $X_H$ is the most significant halve of X, $A_L$ is the least significant halve of A and $X_L$ is the least significant halve of X.

The partial products from the smaller multiplier blocks should be correctly arranged and accumulated by fast multi-operand adders. A scheme of implementing a 8 bit multiplier using four $4\times 4$ multipliers is shown below in Figure 1.

Figure 1: Implementation of 8-bit multiplier using two 4-bit multipliers

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