XOR Gate

The XOR (Exclusive OR) gate configuration is extremely simple to spot, however if you are new to it, then you might as well stare at the circuit diagram for a few minutes because in digital electronics you come across this all the time. Almost all textbooks have it, and it even turns up in GCSE exams masquerading as a question. Let us assume that they give you the logic circuit diagram and your task is to build a Boolean expression that describes this circuit. In addition, you should also simplify it to the standard well-known form for XOR gates.

XOR Truth Table

Boolean Implementation

This circuit is a straightforward implementation of the XOR function utilising the NAND, AND, and OR gates. We first write down the boolean expressions for the intermediate terms.

We start by substituting for the C and D terms in Q, and notice that there is that familiar De Morgan term that we can substitute for as well.

We open up the brackets, and end up making a longer expression.

Luckily, we can use these Boolean rules to simplify the expression, and after simplification, we end up with 0's in the formula. However, we can eliminate them as they are part of the OR function.

Therefore, we end up with the famous XOR identity.

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