UNIT B.5 — COMPUTING

Boolean algebra and logic gates

BRIDGE · EE Foundations Bridge · ~10 min

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Boolean algebra is math with only two values: 1 (true, on, energized) and 0 (false, off, dead). Three operations build everything: AND (output 1 only if all inputs are 1), OR (output 1 if any input is 1), NOT (invert). A truth table lists the output for every input combination — the digital equivalent of a wiring diagram.

You have wired Boolean logic already. Two switches in series feeding a load is an AND gate — both must close. Two switches in parallel is OR — either one energizes the load. Your 3-way switch circuit (Sandbox exercise 03) is an XOR in disguise: the light state flips whenever either switch flips.

One more idea unlocks computing: NAND (AND then NOT) is *universal* — any logic function whatsoever can be built from NAND gates alone. Chain millions of them and you have a processor. That is not a metaphor; it is literally how CPUs are constructed.

Go deeper: MIT's Computation Structures, and the famous Nand2Tetris course where you build a working computer starting from NAND gates — Semesters 1 and 3 of the Go Deeper pathway.

AND

Switches in series

Switches in parallel

NAND

Universal gate

Knowledge check

Quiz — 3 questions

1. Two switches wired in series feeding a lamp implement:

2. An OR gate outputs 0 only when:

3. NAND is called a universal gate because:

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