On the study of logarithmic time parallel adders

Abstract

This work formulates a set of equations to describe logarithmic time parallel adders. The equations can be used to explain several popular fast adder schemes and derive new adder schemes easily. It is shown that if there is an adder constructed from conditional-sum rule, then we can always obtain another adder based on carry-lookahead rule with equivalent topology and structure, and vice versa.Index Termsparallel adder, adder algorithm, conditional-sum, and carry-lookahead. I. INTRODUCTIONAddition is an essential operation in many digital signal-processing applications. Fast addition is usually achieved by using logarithmic time parallel adders. Conventionally, logarithmic time parallel adders can be categorized into two classes of algorithms, carry-lookahead and conditional-sum. However, it is hard to compare their performance and determine the circuit complexity for each adder scheme. Another disadvantage of such classification is that different optimization technique has to be developed for each adder type. Four popular logarithmic time parallel time schemes, including canylookahead adder (CLA)[ 11, ELM adder (ELMA)[2][3], conditional-sum adder (CSMA)[4], and conditional-carry adder (CCA)[S], are discussed herein. Three ternary operators are defined to simplify the analysis, and a set of equations using the defined operators is developed to describe these adders. These equations show that the performance of each adder scheme can be determined and be compared by 0-7803-6488-O/OO/$lO.OO 0 2000 IEEE