If the operation of a circuit is defined by a Boolean expression, a logic-circuit diagram can he implemented directly from that expression.

Suppose that we wanted to construct a circuit whose output is y = AC+BC' + A'BC.

This Boolean expression contains three terms (AC, BC', A'BC), which are ORed together.

This tells us that a three-input OR gate is required with inputs that are equal to AC, BC', and A'BC, respectively.

Each OR-gate input is an AND product term, which means that an AND gate with appropriate inputs can be used to generate each of these terms. Note the use of INVERTERs to produce the A' and C' terms required in the expression.