Logic Gates

Controlling electricity gives us the ability to make yes and no decisions or true and false. By combining two signals, we can give a single true or false answer, depending on the logic. The flow of electricity is controlled using gates (no, not named after Bill Gates - like a gate).

Standard Logic Gate Symbols
NOT
AND
NAND
OR
NOR
XOR
XNOR
All Truth Tables
NOT

The simplest gate, this item inverts or reverses the signal. Q=AQ= \overline A

Input (A)

Output (Q)

0

1

1

0

AND

Only outputs true if both inputs are true. Q=AB or A×BQ = A \cdot B \text{ or } A \times B

A

B

Output (Q)

0

0

0

0

1

0

1

0

0

1

1

1

NAND

Any gate with a dot is an inverted gate. Q=AB or A×BQ = \overline{A \cdot B} \text{ or } \overline{A \times B} This is the NOT AND gate:

A

B

Output (Q)

0

0

1

0

1

1

1

0

1

1

1

0

OR

One or the other or both! Q=A+BQ = A+B

A

B

Output (Q)

0

0

0

0

1

1

1

0

1

1

1

1

NOR

Very simply NOT OR. Q=A+BQ = \overline{A+B}

A

B

Output (Q)

0

0

1

0

1

0

1

0

0

1

1

0

XOR

Exclusive OR meaning only one is true, not both. Q=ABQ = A \bigoplus B

A

B

Output (Q)

0

0

0

0

1

1

1

0

1

1

1

0

XNOR

Exclusively NOT OR. If both inputs are the same, output true. Q=ABQ = \overline{A \bigoplus B}

A

B

Output (Q)

0

0

1

0

1

0

1

0

0

1

1

1

All Truth Tables

A

B

AND

NAND

OR

NOR

XOR

XNOR

0

1

0

1

0

1

0

1

0

1

0

1

1

0

1

0

1

0

0

1

1

0

1

0

1

0

1

0

1

0

0

1

Individually:

The two "universal" gates are NOR and NAND - it is said that you can create all the other logic gates with a combination of just these two.

There are tons of videos available about logic gates. If I had to pick a favourite, my current is this one, although she talks incredibly fast and you might need to slow it down or rewind.