De Morgan demo

Two circuits, two expressions, one truth table — and two lamps that always agree. A ready-made basics circuit you can open in the TorchAnvil simulator.

Two ways to say the same thing

De Morgan's laws are two tiny algebraic identities that show up all over digital design:

• !(A & B) = !A | !B
• !(A | B) = !A & !B

This sample builds the first one as two parallel circuits driven by the same two levers, each ending at its own lamp. The claim is: the lamps always, always agree.

How it works

There are two independent chains:

• Top chain: A and B feed an AND, then a NOT. The top lamp shows !(A & B) — "it's NOT the case that both are on."
• Bottom chain: A goes through a NOT. B goes through a NOT. Those two negated signals feed an OR. The bottom lamp shows !A | !B — "at least one of them is off."

Each lever fans out to both chains, so the two circuits always see identical inputs.

A	B	A & B	!(A & B)	!A	!B	!A OR !B
0	0	0	1	1	1	1
0	1	0	1	1	0	1
1	0	0	1	0	1	1
1	1	1	0	0	0	0

The fourth and seventh columns match on every row. That's the law, in the flesh.

Why it matters

De Morgan is the "flip it around" trick that lets you rewrite any Boolean expression in a more convenient form. Designers use it constantly:

• To push NOTs through gates when optimizing for chip area.
• To convert an OR-based design into a NAND-based one (cheaper to fabricate) without changing behavior.
• To reason about inverted signals when debugging.

Seeing the two forms side by side — and watching them stay locked in step — makes the law intuitive rather than abstract.

Try this

• Cycle through all four lever combinations. Both lamps turn off at exactly the same moment (1, 1) and both are on the other three times.
• Block one wire in your head: imagine only the top chain exists. Now only the bottom. Same answers, different paths.
• This circuit has no connections between the two chains. They share only the two levers — everything else is independent.