Digital Logic Design

The world is analog, but the machine is digital — why every modern system thinks in 1s and 0s.

One idea — place value — writes the same number in decimal, binary and hex.

The same number, translated between decimal, binary and hexadecimal.

The simplest thing a computer does with numbers — four rules and a carry.

There is no minus-sign wire in a chip — this is how negatives are encoded.

Integers can't hold 6.625 — the two ways a machine represents real numbers.

Where it all pays off — a single byte is a chip's control panel.

The three primitive gates and the algebra that describes them.

The complete, unambiguous way to describe what a logic circuit does.

Four more gates from the first three — and the two that can build anything.

The algebra rules that shrink an expression — fewer gates, less power.

The single most useful identity in digital design — pushing a NOT through a group.

Turn a written requirement — a safety rule — into logic you can build.

How to write any Boolean function in a complete, standard form.

A visual puzzle that turns a long truth table into the shortest circuit.

Inputs that can never happen are free simplification — use them.

A repeatable recipe: turn a sentence into a working circuit.

The circuit that adds binary, carries and all — built from gates.

Line up full adders, each carry feeding the next — add many bits at once.

One control bit turns your adder into a subtractor too — no second circuit.

A circuit that returns a verdict: is A bigger than, equal to, or less than B?

Blocks that move data instead of computing it — select one of many.

Turn a compact binary code into one active line — and back again.

Every block in this stage was practice for one machine: the arithmetic logic unit.