Truth Tables and Simplifying Expressions

From a table of results to the smallest circuit.

A truth table lists every combination of inputs and the output required for each. From the rows that give 1 you can write a sum-of-products expression, with one AND term for each such row, all joined by OR.

Boolean laws then shrink the expression. For example, combining A·B with A·B' gives just A, and the absorption law says A + A·B equals A. Fewer terms means fewer gates, lower cost and less power.

• Count rows as 2 raised to the number of inputs.
• Karnaugh maps give a visual way to simplify.
• Always verify the simplified form.

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