Example
While there are many ways to minimize a circuit, this is an example that minimizes (or simplifies) a boolean function. Note that the boolean function carried out by the circuit is directly related to the algebraic expression from which the function is implemented. Consider the circuit used to represent . It is evident that two negations, two conjunctions, and a disjunction are used in this statement. This means that to build the circuit one would need two inverters, two AND gates, and an OR gate.
We can simplify (minimize) the circuit by applying logical identities or using intuition. Since the example states that A is true when B is false or the other way around, we can conclude that this simply means . In terms of logical gates, inequality simply means an XOR gate (exclusive or). Therefore, . Then the two circuits shown below are equivalent:
You can additionally check the correctness of the result using a truth table.
Read more about this topic: Circuit Minimization
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