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Logic gates
[A logic gate consists in] three connections where there may or may not be some electricity. Two of those connections are places where electricity may be put into the device, and the third connection is a place where electricity may come out of the device. (Scott, 2009 p.21)
Logic gates are the basic building blocks of digital computing. A logic gate is an electrical circuit that has one or more than one input and only one output. The input controls the output and the logic determining which types of input (on/off) lead to specific outputs (on/off) is identical to the truth-conditions of the Boolean connectives specifiable in terms of truth-tables. Physically, what 'travels through' the gates is electrical current and what constitutes the 'gate' is a transistor responding to the current. At the next level of abstraction it is bits that go into the gate and bits which come out: binary information that may be either 1 or 0.
NOT gate
The NOT gate inverts the value of whatever input it receives
Symbol
Truth conditions
| P | ~ P |
|---|---|
| T | F |
| F | T |
Interactive circuit
AND gate
The AND gate represents the truth conditions of the conjunction truth functional connective
Symbol
Truth conditions
| P | Q | P & Q |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
Interactive circuit
NAND gate
The NAND gate inverts the truth conditions of AND.
Symbol
Truth conditions
| P | Q | ~(P & Q) |
|---|---|---|
| T | T | F |
| T | F | F |
| F | T | F |
| F | F | T |
Interactive circuit
NAND is a universal logic gate: equipped with just a NAND we can represent every other possible logical condition. In practice with circuits, it is more efficient to use specific dedicated gates (i.e OR, AND, NOT etc) for the other Boolean connectives but in principle the same output can be achieved through NANDs alone.
OR gate
The OR gate represents the truth conditions of the disjunction truth functional connective
Symbol
Truth conditions
| P | Q | P v Q |
|---|---|---|
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |
Interactive circuit
XOR gate
The OR gate represents the truth conditions of the exclusive OR
Symbol
Truth conditions
| P | Q | ~(P <> Q) |
|---|---|---|
| T | T | F |
| T | F | T |
| F | T | T |
| F | F | F |
Interactive circuit
NOR gate
The NOR gate inverts the function of an OR gate
Symbol
Truth conditions
| P | Q | P v Q |
|---|---|---|
| T | T | F |
| T | F | F |
| F | T | F |
| F | F | T |
Interactive circuit
References
Scott, J. Clark. 2009. But how do it know?: the basic principles of computers for everyone. Self-published.