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ON MULTIPLE OPERANDS ADDITION OF SIGNED BINARY NUMBERS

IP.com Disclosure Number: IPCOM000128289D
Original Publication Date: 1977-Dec-31
Included in the Prior Art Database: 2005-Sep-15
Document File: 4 page(s) / 18K

Publishing Venue

Software Patent Institute

Related People

Dharma P. Agrawal: AUTHOR [+4]

Abstract

Recent application of negabinary number systems in signal processing has evoked the question of suitability of binary base. Many proposals for multioperand addition of unsigned binary numbers are available in the literature. Here, 2's complement method of performing arithmetic on two operands has been extended for n signed summands. The time delay remains the same as that of processing n unsigned numbers. This method shows new promises for its application to signal processing.

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THIS DOCUMENT IS AN APPROXIMATE REPRESENTATION OF THE ORIGINAL.

ON MULTIPLE OPERANDS ADDITION OF SIGNED BINARY NUMBERS*

Dharma P. Agrawal T. R. N. Rao

Computer Science Department Southern Methodist University Dallas, Texas August, 1977

*This work is supported by the National Science Foundation Grant ENG76-11237 and ONR Grant N00014-77-C-0455.

Abstract

Recent application of negabinary number systems in signal processing has evoked the question of suitability of binary base. Many proposals for multioperand addition of unsigned binary numbers are available in the literature. Here, 2's complement method of performing arithmetic on two operands has been extended for n signed summands. The time delay remains the same as that of processing n unsigned numbers. This method shows new promises for its application to signal processing.

Index Terms: 2's complement extension digits, multioperands, negabinary, overflow, signal processing, signed numbers.

Introduction

Recently, applications of negabinary systems for signal processing [11-[31 and other areas [4],
(5] has been advocated on the grounds that it has a sign-independent representation and hence is suitable for simultaneous addition of several numbers. Many papers [6]-[8] have dealt with multiple operands addition of unsigned binary numbers. But, relatively little-has appeared on the addition of signed binary numbers. Here we have extended the additive algorithms of two numbers in 2's complement system to addition of multiple operands. Required modifications are also derived and practical implementation steps are clearly indicated.

Word-Length Extension Requirement,

In 2's complement number system, the most significant bit (MSB) always indicates the sign. Let a number A be denoted by the k-tuple A as

(Equation Omitted)

Let S be the sum of n such numbers. A simplest approach to this is to consider each operand as having an extended word-length r (r > k), such that all possible sums of n numbers can be accommodate by the r-bit 2's complement system.

Clearly the extension required will be

Southern Methodist University Page 1 Dec 31, 1977

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ON MULTIPLE OPERANDS ADDITION OF SIGNED BINARY NUMBERS

(Equation Omitted)

, (3) where Fxj denotes the smallest integer not less than x.

Addition Algorithm

As discussed in the previous section, the addition of n numbers each having k bits, requires a sum in r-bit system if overflow is to be avoided. So we convert all numbers to r bit system. This is simply done by aug-menting the original numbers by (r-k) sign extension bits, i.e., by adding (r-k) O's for positive numbers and I's for negati ve numbers. This does not change their numerical value in 2's complement system (see Table 1 for this extension). Then the sum S can be obtained by adding extended n numbers and throwing away all carry overflows from the (r- l)th stage. (Note that the carry from the (r-l)th stage has a weight 2 r , which equals 0 in the r-bit 2's complement system.)

In order t...