Abstract

In this paper, we present a modified addition algorithm modulo m with a signed-digit(SD) number representation where m = 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> −1, 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> or 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> +1. To simplify an SD full adder, new addition rules are proposed for generating the intermediate sum and carry with a binary number representation. By using the new codes for intermediate sum and carry and the end-around carry architecture, the proposed modulo m addition requires less hardware and short delay time for the residue addition than previous methods. Compared to previous work, the circuit area and delay time are improved by 21% and 30%, respectively.

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