From one switch to a thinking machine

A single transistor switches a current. Wire two together properly and you get a logic gate — a device that takes one or more 1/0 inputs and produces a 1/0 output according to a simple rule. Wire enough gates together and you get arithmetic, memory, and eventually an entire processor. This is the bridge between physics and computing.

Key Concept

Logic Gate

A small circuit (usually 2–6 transistors) that implements a Boolean function: output is HIGH (1) or LOW (0) based on the combination of inputs. The basic primitive of every digital chip.

Key Concept

Truth Table

A complete enumeration of input combinations and their resulting outputs. For a 2-input gate, that's just 4 rows — yet from these tiny tables, every program you've ever run is built.

Key Concept

Boolean Logic

The algebra of true/false (1/0) values, formalized by George Boole in 1854. Claude Shannon showed in 1937 that switching circuits implement Boolean algebra exactly — the conceptual foundation of digital electronics.

Key Concept

NOT Gate (Inverter)

One input, one output. Output is the logical inverse of input: NOT 0 = 1, NOT 1 = 0. Built from one pMOS + one nMOS transistor. The simplest possible logic gate.

Key Concept

AND Gate

Output is 1 only when ALL inputs are 1. Like two doors in series — both must be open. In CMOS we usually build AND as NAND followed by NOT.

Key Concept

OR Gate

Output is 1 if ANY input is 1. Like two doors in parallel — either path lets you through.

Key Concept

NAND Gate

AND followed by NOT — output is 0 only when all inputs are 1. The cornerstone of CMOS design because it's the simplest universal gate.

Diagram · Logic gate playground

interactive

CMOS Schematic — NAND

Truth Table

A	B	Y
0	0	1
0	1	1
1	0	1
1	1	0

NAND is universal — every other gate can be built from NANDs alone.

Pick a gate, toggle inputs A and B, watch the truth table row light up and the underlying CMOS transistors flip ON/OFF.

Light switches

**NOT** is a switch wired backwards — flip ON, the lamp goes OFF. **AND** is two switches in series feeding one lamp — both must be on. **OR** is two switches in parallel — either one lights it up. **NAND** is AND with the bulb wired backwards — it lights up unless both switches are flipped.

Checkpoint · +5 XP

NAND inputs (1, 1) produce output:

Why NAND is special. Mathematically, NAND is functionally complete: any Boolean function — AND, OR, XOR, an entire CPU — can be built from nothing but NAND gates. Combine that with the fact that NAND is dirt-cheap in CMOS (4 transistors, fast, low power) and you have the reason almost every chip is, deep down, an enormous sea of NANDs.

Try It Yourself

Build a circuit from logic gates

Open the Chip Builder, drag in a NAND gate, click 'Peek Inside' to see the underlying transistors, then power it on and toggle the inputs. Try building an AND gate from two NANDs.

Open Chip Builder

Lesson Summary

Combine a few transistors and you get a logic gate — the atom of digital computing.
The five core gates: NOT, AND, OR, NAND, NOR.
Every gate has a truth table: a tiny lookup of outputs for every possible input combination.
NAND is universal — give an engineer enough NAND gates and they can build any digital circuit, including a CPU.

Test Your Knowledge · +50 XP

An AND gate outputs 1 when:

A NOT gate of input 1 produces:

Why is NAND called 'universal'?

An OR gate is most like:

A truth table for a 2-input gate has how many rows?