Identity Law

Whereas elementary algebra applies to numbers, Boolean algebra is about truth values True and False, or 1 and 0, and the results obtained by acting on them with AND, OR and NOT operators. Every digital computer uses Boolean algebra; all calculations are based on processing arrays of 1s and 0s.

Early automation systems comprised arrays of hard-wired AND, OR and NOT gates that could logically process True and False input states to generate control outputs that also had either a true or false state. Example: if a tank’s temperature switch AND level switch are on, start the transfer pump. Microprocessors were first developed as programmable and therefore more flexible versions of these early gate arrays.

A set of Boolean laws has been developed that can be used to simplify the design of gate arrays, particularly by reducing the number of gates need to fulfil a particular function. Each law has a name, and is expressed in terms of one or more Boolean expressions.

The Identity Law is one of the Boolean Laws; it has two expressions:

1 AND A = A - the product of 1 and any number or variable is the number or variable itself


0 OR A = A - the sum of 0 and any number or variable is the number or variable itself