VLSI implementation of fast addition using quaternary Signed Digit number system

Dubey, Sanjay; Rani, Reena; Kumari, S.; Sharma, Neelam

doi:10.1109/ice-ccn.2013.6528581

Cited by 8 publications

(1 citation statement)

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“…Now studies on optical computing algorithms and techniques have been made much progress and the optical computing modes have shown remarkable advantages in meeting the requirements such as parallel, carry-free, and fast computing. According to the value of the radix, the signed-digit representation contains the subsets of MSD number [5], [8], [9], [10], [11], trinary [2], [3], [12], [13], quaternary [14], [15], [16] and negabinary signed-digit number [17], and so on. According to the steps of optical computing, the MSD additions are now usually classified in terms of the number of steps involved, i.e., three-step [5], [8], [9], [10], [11], twostep [12], [13], [14], [18], [19], [20] and one-step algorithms [17], [21], [22], [23], [24].…”

Section: Introductionmentioning

confidence: 99%

Characteristics of Parallel Carry-Free Three-Step MSD Additions

et al. 2021

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Since the modified signed digital (MSD) redundant representation was proposed in the 1950s, lots of achievements have been made in MSD arithmetic. By inspecting the processes of the parallel carryfree three-step MSD addition, the transformations for such additions are studied in detail in this paper. The characteristics for parallel carry-free three-step MSD addition are proposed and the correctness is proved. Then seven groups of transformations that have characteristics of three-step MSD addition are presented. These groups of transformations are dual or self-dual, and some of them have simpler forms than the typical transformations consisting of T, W, T , W , T 2. The general design mode of parallel carryfree three-step MSD additions and its applications in ternary optical computer (TOC) are further proposed. At the same time, single adder (multi-adder) reconstruction mode, processor bits allocation strategy, and light path diagrams are given. The optical experiments of MSD additions for three groups of MSD addition transformations show that the results of these transformations are correct. This work provides the theoretical basis for the design of the ternary optical computer adder.

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