Browse Prior Art Database

Unit to Square a Number in Reduced Time and Area

IP.com Disclosure Number: IPCOM000122652D
Original Publication Date: 1991-Dec-01
Included in the Prior Art Database: 2005-Apr-04
Document File: 2 page(s) / 83K

IBM

Related People

Bailey, CA: AUTHOR

Abstract

Disclosed is a method and device to square a number which uses less circuit area and less circuit delay than traditional methods.

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This is the abbreviated version, containing approximately 52% of the total text.

Unit to Square a Number in Reduced Time and Area

Disclosed is a method and device to square a number which
uses less circuit area and less circuit delay than traditional
methods.

Certain complex arithmetic functions that need to be
implemented in computer hardware can benefit from the use of a unit
to square a number.  For example, to produce a reciprocal by the
Newton-Raphson Technique requires the evaluation of 2X-SQR(X)B
several times, where X and B are binary numbers and SQR(X) is X*X.
While this function SQR(X) can be implemented with a standard
multiply unit, multiplying 2 numbers requires a large amount of chip
area and takes a relatively long amount of time due to the required
levels of logic (gate delays).

The following is a description of a unit to square an eight-bit
number.  Enough detail is included so that the same technique can be
extended to longer length numbers.  A formula is also included to
predict the size of the hardware needed to implemented longer
numbers.

In standard multiplication, logical products are created by
multiplying and shifting a multiplicand depending on multiplier bits.
(See Fig. 1.)  There are several commonly used techniques that reduce
the number of logical products by shifting the multiplicand based on
2 or more bits of the multiplier (*).  The technique described here
reduces the number of logical products without the overhead of
shifters and control logic.

In "Fig 'SQUARE' unknown" an 8-bit number is squared, but this
can easily be extended to work for any length input.  The reduced
logical products can be determined b...