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eolas/Hardware/Logic_Gates/Nand_gate.md
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tags
Logic
Electronics
Hardware
logic_gates

NAND gate

A NAND gate is a logic gate that inverts the truth-conditions for AND.

A real-life circuit showing two switches corresponding to two transistors which control the LED light:

NAND_from_transitors.png

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.

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:

NAND.png

The diagram below shows how the circuit models the truth conditions for NAND

Diagram representing NAND gate:

NAND.gif

  • 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.