Computer Arithmetic by Mircea Vlăduţiu

Author:Mircea Vlăduţiu
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

Obviously, in a similar manner, one can configure multipliers for 3n×3n bits, 4n×4n bits, etc., on the basis of constructive blocks for n×n bit multiplication [ErLa04].

3.A special case is squaring, and, by extension, exponentiation. Any of the presented multiplication devices can execute the operation P=X 2, where we have the multiplicand Y=X. However, in case squaring and, generally, exponentiations are more frequent, it is usually worth investing in a dedicated multiplier “built in” to the hardware, because its cost is reduced and its delay is lower than that of a universal multiplication device.

The simplification brought about by a device dedicated to squaring can be ascertained if we revert to the example given by (3.24), where Y will be substituted by X, let us intervene in relation (3.26) by taking into account that x i x i =x i and x i x j =x j x i . Consequently, the following will be obtained:

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