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 framework for these fundamental circuits.

Contribution

It introduces a novel modeling approach using pseudoboolean differential calculus for ideal latches and flip-flops, including interconnected circuits.

Findings

Derived equations for various ideal latch circuits

Provided a unified mathematical framework for digital latches

Enhanced understanding of circuit behavior through equations

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.