56 lines
1.7 KiB
Markdown
56 lines
1.7 KiB
Markdown
---
|
|
categories:
|
|
- Computer Architecture
|
|
- Electronics
|
|
- Hardware
|
|
tags: [logic-gates, binary]
|
|
---
|
|
|
|
# NAND gate
|
|
|
|
A NAND gate is a logic gate that inverts the truth-conditions for `AND`.
|
|
|
|
Diagram representing NAND gate:
|
|
|
|
<img src="/home/thomas/repos/computer_science/img/NAND.png" width="180" />
|
|
|
|
The diagram below shows how the circuit models the truth conditions for `NAND`
|
|
|
|
<img src="/home/thomas/repos/computer_science/img/NAND.gif" width="400" />
|
|
|
|
- When both switches are off (corresponding to `false` `false`) the output is on (the bulb lights up).
|
|
- If either one of the switches are on, the output remains on (corresponding to `true` `false` or `false` `true` )
|
|
- It is only when both switches are on, that the output is off (corresponding to `true` `true` )
|
|
|
|
This is the exact opposite to the truth-conditions for AND.
|
|
|
|
## Transliterating the logic truth-table to the switch behaviour
|
|
|
|
We can now present a truth table for NAND along side that for AND:
|
|
|
|
```
|
|
A B Output
|
|
_ _ _____
|
|
|
|
f f t
|
|
t f t
|
|
f t t
|
|
t t f
|
|
|
|
A B Output
|
|
_ _ _____
|
|
t t t
|
|
t f f
|
|
f t f
|
|
f f f
|
|
```
|
|
|
|
We can see that it inverts the value of AND.
|
|
|
|
## Significance of the NAND gate: functional completeness
|
|
|
|
> **Equipped with just a NAND we can represent every other possible logical condition within a circuit.**
|
|
|
|
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.
|
|
|
|
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.
|