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In Boolean algebra, circuit minimization is the problem of obtaining the smallest logic circuit (Boolean formula) that represents a given Boolean function or truth table. The unbounded circuit minimization problem was long-conjectured to be
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Purpose
The problem with having a complicated circuit (i.e. one with many elements, such as logical gates) is that each element takes up physical space in its implementation and costs time and money to produce in itself. Circuit minimization may be one form of logic optimization used to reduce the area of complex logic in integrated circuits.
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
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
You can additionally check the correctness of the result using a truth table.