Logical operations in computers are also called "Boolean operations", which are: AND , OR , NOT , and XOR . In addition, there are: same or , NAND , NOR in the gate circuit . There are seven types in total.
Among these seven logical operations, only the logical NOT operation is a unary logical operation (one operand), and the other six are binary logical operations (two operands).
Logical operations have only two Boolean values:
- 0, indicating a false value (False).
- 1, indicating the true value (True).
1. AND(AND)&
Logical expression: F=AB
Logical AND operation, operation rules: all 1s are 1, and 0s are 0 . That is, the result is 1 only when both operands are 1, and 0 in other cases (it can also be said that as long as there is 0, the result is 0).
| Operand 1 | Operand 2 | result value |
|---|---|---|
| 1 | 1 | 1 |
| 1 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 0 | 0 |
2. 或（OR）|
Logical expression: F=A+B.
(Also written as A∨B (logic), A || B (computer science), or A + B (electronics))
Logical OR operation, operation rules: all 0s are 0, and 1 is 1 . That is, the result is 0 only when both operands are 0, and 1 in other cases (it can also be said that as long as there is 1, the result is 1).
| Operand 1 | Operand 2 | result value |
|---|---|---|
| 1 | 1 | 1 |
| 1 | 0 | 1 |
| 0 | 1 | 1 |
| 0 | 0 | 0 |
3. NOT (NOT)~
Logical expression:
Logical NOT operation has only one operand, so it is a unary logical operation.
Operation rules: 1 changes to 0, 0 changes to 1 . That is, when the operand is 1, the result is 0, and when the operand is 0, the result is 1.
| operand | result value |
|---|---|
| 1 | 0 |
| 0 | 1 |
4. Exclusive OR (XOR)^
Logical expression:
logical XOR operation, operation rules: difference is 1, sameness is 0 . That is, the result is 1 when the two operands are different, and the result is 0 when the two operands are the same.
| Operand 1 | Operand 2 | result value |
|---|---|---|
| 1 | 1 | 0 |
| 1 | 0 | 1 |
| 0 | 1 | 1 |
| 0 | 0 | 0 |
5. XNOR
Logical expression:
Logical same-or operation, operation rules: the same is 1, the difference is 0 . Contrary to the rules of XOR operation. That is, the result is 1 when the two operands are the same, and the result is 0 when the two operands are different.
| Operand 1 | Operand 2 | result value |
|---|---|---|
| 1 | 1 | 1 |
| 1 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 0 | 1 |
6. NAND
Logical expression:
logical AND and NOT operation, operation rules: AND first and then NOT (all 1s are 0s, and 0s are 1) . That is to say, first perform a "logical AND operation" on the two operands, and then perform a "logical NOT operation" on the AND "operation result value" to produce the final result.
| Operand 1 | Operand 2 | AND operation result value | final result value |
|---|---|---|---|
| 1 | 1 | 1 | 0 |
| 1 | 0 | 0 | 1 |
| 0 | 1 | 0 | 1 |
| 0 | 0 | 0 | 1 |
7. NOR
Logical expression:
logical OR operation, operation rules: OR first and then NOT (all 0s are 1, and 1 is 0) . That is, perform a "logical OR operation" on the two operands first, and then perform a "logical NOT operation" on the "OR operation result value" to produce the final result.
| Operand 1 | Operand 2 | OR result value | final result value |
|---|---|---|---|
| 1 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 0 | 1 | 1 | 0 |
| 0 | 0 | 0 | 1 |