A universal gate can build every Boolean function when enough copies are combined. NAND and NOR each qualify. Start by making NOT, then construct AND and OR using inversion and De Morgan's laws. This gives a systematic route from an expression to one gate type.
Worked example
Join both inputs of a NAND to A: its output is NOT A. To build A AND B, first NAND A and B, then invert that output with another tied-input NAND. To build A OR B, NAND the separately inverted inputs A and B.
What to watch for
Logical equivalence does not mean equal delay, power or electrical drive. Count the additional stages when comparing an implementation with the original expression.
Try it yourself
How can one NOR gate act as an inverter?
Answer: Tie its inputs together. Its output is NOT(A OR A), which simplifies to NOT A.
How to study this topic
Begin with settled Boolean values, then consider the physical signal and the device's electrical limits. A logic symbol explains a function; its data sheet explains which voltages, currents and delays are permitted.
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