NOT
Inverter
¬a
the output is the opposite of the input
| a | f |
|---|---|
| 0 | 1 |
| 1 | 0 |
Gate Reference
Gate reference
Six basic gates, each from three angles: expression, truth table and symbol. Click any row of a truth table and the pin values on the symbol follow.
The “basic gates” here are the digital-logic view: AND, OR and NOT are the primitives, with NAND and NOR listed for their universality. In Boolean algebra the primitives are ∧, ∨ and ¬; in CMOS they are NAND, NOR and the inverter — an AND is usually NAND plus inverter.The same gate at four levels →
GateTruth tableSymbol
AND
Conjunction
a ∧ b
the output is 1 only when both inputs are 1
| a | b | f |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
OR
Disjunction
a ∨ b
the output is 1 when either input is 1
| a | b | f |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
XOR
Exclusive or
a ⊕ b
the output is 1 when the inputs differ
| a | b | f |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
NAND
¬(a ∧ b)
the output is 0 when both inputs are 1
| a | b | f |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
NOR
¬(a ∨ b)
the output is 1 only when both inputs are 0
| a | b | f |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |
Click any row of a truth table and the pin values on the symbol to the right follow.