Logic operators — Foundations

The "Logic operators" chapter introduces the various calculation and storage operators found in complex electronic systems, particularly computers. The essential characteristic of these operators is that they work on quantized data (digital or numerical) using only 0 or 1 values, as opposed to analog circuits and operators, which work on continuous data.

In this first article, we present the mathematical foundations and implementation of combinatorial logic operators. Boolean algebra provides the mathematical basis for processing quantized information, and for realizing the various hardware operators that perform this processing. Logic gates (basic logic components) are associated with the various operators of Boolean algebra. Combinatorial function synthesis methods enable more complex processing operators, such as decoders, multiplexers, adders, arithmetic and logic units, multipliers, etc., to be created from fundamental hardware operators, ranging from logic gates to universal operators such as ROMs and programmable logic arrays (PLA, PAL, etc.). Arithmetic operators are a good example of these combinatorial operators.

A second article deals with flip-flops, based on elementary logic gates, which are used to build registers and automata [ ]. A third article [ ].