65 lines
2.1 KiB
Markdown
65 lines
2.1 KiB
Markdown
---
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tags:
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- Logic
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- Electronics
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- Hardware
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- logic_gates
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---
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# NAND gate
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A NAND gate is a logic gate that inverts the truth-conditions for `AND`.
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A real-life circuit showing two switches corresponding to two transistors which control the LED light:
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In this circuit, there are two transistors, each connected to a switch. The switches control the LED light. So the switches are the input and the LED is the output.
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For clarity, we are not going to draw both transistors, we will simplify the diagram with a symbol for them which stands for the NAND gate:
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The diagram below shows how the circuit models the truth conditions for `NAND`
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Diagram representing NAND gate:
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* When both switches are off (corresponding to `false` `false`) the output is on (the bulb lights up).
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* If either one of the switches are on, the output remains on (corresponding to `true` `false` or `false` `true` )
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* It is only when both switches are on, that the output is off (corresponding to `true` `true` )
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This is the exact opposite to the truth-conditions for AND.
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## Transliterating the logic truth-table to the switch behaviour
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We can now present a truth table for NAND along side that for AND:
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```
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A B Output
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_ _ _____
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f f t
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t f t
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f t t
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t t f
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A B Output
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_ _ _____
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t t t
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t f f
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f t f
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f f f
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```
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We can see that it inverts the value of AND.
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## Significance of the NAND gate: functional completeness
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> **Equipped with just a NAND we can represent every other possible logical condition within a circuit.**
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In practice, 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.
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When we add more NAND gates and combine them with each other in different ways we can create more complex output sequences and these too will have corresponding truth tables.
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