Logic gates
Introduced| English | Meaning |
|---|---|
| Boolean logic/ˈbuːlɪən ˈlɒdʒɪk/ | Reasoning and operations using the two truth values true and false. |
| logic gate/ˈlɒdʒɪk ɡeɪt/ | A device or operation that applies a Boolean rule to one or more inputs to produce an output. |
| truth table/truːθ ˈteɪbl/ | A table listing the output of a logical expression or circuit for every combination of inputs. |
| inverted/ɪnˈvɜːtɪd/ | inverted |
The building blocks of circuits
- Boolean logic 布尔逻辑 works with values that are true (1) or false (0).
- A logic gate 逻辑门 takes inputs and gives one output by a fixed rule.
- A truth table 真值表 lists every input combination and its output.
The six gates
- You must know six: NOT, AND, OR, NAND, NOR, XOR.
- NOT has one input; the rest have two. A small circle on the output means inverted 取反 (NOT, NAND, NOR).
AND outputs 1 only when both inputs are 1
Logic gates
output from the truth table
Toggle A and B through each gate and read the result off the truth table.
NOT, AND, OR
- NOT reverses the input. AND is 1 only when both inputs are 1. OR is 1 when at least one input is 1.
| A | B | A AND B | A OR B |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 1 |
(NOT: 0→1, 1→0.)
A real logic chip: inside are logic gates like the ones on this page
An AND gate gives output 1 when:
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AND outputs 1 only when every input is 1.
An OR gate gives output 0 only when:
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OR is 1 if at least one input is 1, so it is 0 only when both are 0.
NAND, NOR, XOR
- NAND = opposite of AND; NOR = opposite of OR; XOR = 1 when the inputs are different.
| A | B | A NAND B | A NOR B | A XOR B |
|---|---|---|---|---|
| 0 | 0 | 1 | 1 | 0 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 1 | 0 | 1 |
| 1 | 1 | 0 | 0 | 0 |
The six logic gates. A small circle on the output means the result is inverted (NOT, NAND, NOR).
A XOR gate gives output 1 when:
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XOR (exclusive OR) is 1 when the inputs differ.
Match each gate to when its output is 1.
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AND = all 1s, OR = any 1, XOR = inputs differ, NAND = NOT AND.
A NOR gate with both inputs 0 gives what output (0 or 1)?
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NOR = NOT OR. OR of (0,0) is 0, so NOR is 1. NOR is 1 only when both inputs are 0.
You've got it
- 1 = true, 0 = false; a truth table lists every input combination
- AND = both 1 · OR = at least one 1 · NOT = invert
- NAND/NOR = AND/OR with the output inverted (the circle)
- XOR = 1 when the inputs differ