Grundlogik
NOT
- Notation
- ¬A, A'
- Programmierung
- Schaltung
- Inverter gate
Beispiel
Reverses a truth value.
If A means logged in, ¬A means not logged in.
Wahrheitstabelle
| A | Out |
|---|---|
| 0 | 1 |
| 1 | 0 |
Informatik-Referenz
Leitfaden zu logischen Operatoren
Verstehen Sie AND, OR, NOT, XOR, NAND, NOR und verwandte Operatoren mit Wahrheitstabellen, boolescher Algebra, digitalen Schaltungen, Programmierung und AI Fragebeispielen.
Grundlogik
AND
- Notation
- A·B, AB
- Programmierung
- Schaltung
- AND gate
Beispiel
True only when every input is true.
isLoggedIn && hasPermission
Wahrheitstabelle
| A | B | Out |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Grundlogik
OR
- Notation
- A+B
- Programmierung
- Schaltung
- OR gate
Beispiel
True when at least one input is true.
isAdmin || isOwner
Wahrheitstabelle
| A | B | Out |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
Abgeleitete Operatoren
XOR
- Notation
- A⊕B
- Programmierung
- Schaltung
- XOR gate
Beispiel
True when the inputs are different.
Half adder sum = A XOR B.
Wahrheitstabelle
| A | B | Out |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
Abgeleitete Operatoren
NAND
- Notation
- ¬(A·B)
- Programmierung
- Schaltung
- NAND gate
Beispiel
The negation of AND. NAND gates can build any Boolean circuit.
A NAND B = NOT (A AND B).
Wahrheitstabelle
| A | B | Out |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
Abgeleitete Operatoren
NOR
- Notation
- ¬(A+B)
- Programmierung
- Schaltung
- NOR gate
Beispiel
The negation of OR. NOR is also functionally complete.
A NOR B is true only when both inputs are false.
Wahrheitstabelle
| A | B | Out |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |
Abgeleitete Operatoren
XNOR
- Notation
- ¬(A⊕B)
- Programmierung
- Schaltung
- XNOR gate
Beispiel
True when the inputs are the same.
A XNOR B behaves like equality for Boolean values.
Wahrheitstabelle
| A | B | Out |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Bitweise Operatoren
Bitwise AND
- Notation
- bit mask
- Programmierung
- Schaltung
- Per-bit AND operation
Beispiel
Applies AND to each bit position. It is different from logical &&.
0101 & 0011 = 0001
Programmierung
Short-circuit evaluation
- Notation
- evaluation rule
- Programmierung
- Schaltung
- Programming evaluation behavior
Beispiel
The second expression may not run if the first expression already determines the result.
user && user.name
Gesetze der booleschen Algebra
Identity laws
A ∧ 1 = A, A ∨ 0 = ACombining with the neutral truth value leaves A unchanged.
Domination laws
A ∧ 0 = 0, A ∨ 1 = 1One fixed input can determine the entire result.
Complement laws
A ∧ ¬A = 0, A ∨ ¬A = 1A statement and its negation cannot both be true, but at least one is true.
De Morgan's laws
¬(A ∧ B) = ¬A ∨ ¬B, ¬(A ∨ B) = ¬A ∧ ¬BMoves a negation across AND or OR while switching the operator.
Absorption laws
A ∨ (A ∧ B) = A, A ∧ (A ∨ B) = AA repeated condition can absorb a more specific condition.