The equations of the ideal latches

TL;DR

This paper develops mathematical equations for ideal digital latches and flip-flops, modeling their behavior using pseudoboolean differential calculus to provide a theoretical foundation for these fundamental circuits.

Contribution

It introduces a novel approach to model ideal digital latches and flip-flops with equations using pseudoboolean differential calculus, enhancing theoretical understanding.

Findings

Derived equations for various ideal latch circuits

Provided a mathematical framework for non-inertial digital circuits

Enhanced theoretical analysis of digital feedback circuits

Abstract

The latches are simple circuits with feedback from the digital electrical engineering. We have included in our work the C element of Muller, the RS latch, the clocked RS latch, the D latch and also circuits containing two interconnected latches: the edge triggered RS flip-flop, the D flip-flop, the JK flip-flop, the T flip-flop. The purpose of this study is to model with equations the previous circuits, considered to be ideal, i.e. non-inertial. The technique of analysis is the pseudoboolean differential calculus.