Some Schemes for Implementation of Arithmetic Operations with Complex Numbers Using Squaring Units

TL;DR

This paper introduces new schemes for complex number arithmetic operations that replace multipliers with squarers, reducing hardware complexity and power consumption in digital circuits.

Contribution

It proposes novel methods for implementing complex arithmetic using squaring units, eliminating the need for multipliers and improving efficiency.

Findings

Reduced hardware complexity compared to traditional methods

Lower power consumption due to use of squarers

Potential for more efficient digital circuit designs

Abstract

In this paper, new schemes for a squarer, multiplier and divider of complex numbers are proposed. Traditional structural solutions for each of these operations require the presence some number of general-purpose binary multipliers. The advantage of our solutions is a removing of multiplications through replacing them by less costly squarers. We use Logan's trick and quarter square technique, which propose to replace the calculation of the product of two real numbers by summing the squares. Replacing usual multipliers on digital squares implies reducing power consumption as well as decreases hardware circuit complexity. The squarer requiring less area and power as compared to general-purpose multiplier, it is interesting to assess the use of squarers to implementation of complex arithmetic.