De Morgan's Theorem: OR with Inverted Inputs = NAND
A + B = A · B
OR with Input Bubbles
=
NAND Gate
Truth Table (Both gates produce identical outputs)
| A | B | Ā | B̄ | Y |
|---|---|---|---|---|
| 0 | 0 | 1 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 1 |
| 1 | 1 | 0 | 0 | 0 |
Click a row to animate both gates
De Morgan's Theorem: AND with Inverted Inputs = NOR
A · B = A + B
AND with Input Bubbles
=
NOR Gate
Truth Table (Both gates produce identical outputs)
| A | B | Ā | B̄ | Y |
|---|---|---|---|---|
| 0 | 0 | 1 | 1 | 1 |
| 0 | 1 | 1 | 0 | 0 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 | 0 |
Click a row to animate both gates
NAND is a Universal Gate
A NAND gate can function as an inverter by tying both inputs together. Since NAND outputs LOW only when both inputs are HIGH, connecting the same signal to both inputs creates inversion.
NAND as Inverter
Y = A · A = A
Inverter Truth Table
| A | Y |
|---|---|
| 0 | 1 |
| 1 | 0 |
Click a row to animate
Because NAND can create an inverter, and combined with itself can create AND and OR gates, NAND is called a universal gate — any logic circuit can be built using only NAND gates.
NOR is a Universal Gate
A NOR gate can function as an inverter by tying both inputs together. Since NOR outputs HIGH only when both inputs are LOW, connecting the same signal to both inputs creates inversion.
NOR as Inverter
Y = A + A = A
Inverter Truth Table
| A | Y |
|---|---|
| 0 | 1 |
| 1 | 0 |
Click a row to animate
Because NOR can create an inverter, and combined with itself can create AND and OR gates, NOR is called a universal gate — any logic circuit can be built using only NOR gates.