Boolean algebra
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Boolean algebra is algebra for binary (0 meaning false, or 1 meaning true). It uses normal maths symbols, but it does not work in the same way. It is named after its creator George Boole.
Contents |
[change] NOT gate
| NOT | |
|---|---|
| 0 | 1 |
| 1 | 0 |
The NOT operator is written with a bar over numbers or letters like this:
It means the output is not the input.
[change] AND gate
| AND | 0 | 1 |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 0 | 1 |
The AND operator is written as 
like this:
The output is true only if one and the other input is true.
[change] OR gate
| OR | 0 | 1 |
|---|---|---|
| 0 | 0 | 1 |
| 1 | 1 | 1 |
The OR operator is written as + like this:
- 0 + 0 = 0
- 0 + 1 = 1
- 1 + 0 = 1
- 1 + 1 = 1
One or the other input can be true for the output to be true.
[change] XOR gate
| XOR | 0 | 1 |
|---|---|---|
| 0 | 0 | 1 |
| 1 | 1 | 0 |
The XOR operator is written as − like this:
- 0 − 0 = 0
- 0 − 1 = 1
- 1 − 0 = 1
- 1 − 1 = 0
[change] Identities
Different gates can be put together in different orders:
is the same as an AND then a NOT. This is called a NAND gate.
It is not the same as a NOT then an AND like this: 
- A + 1 = 1
[change] De Morgans theorem
Augustus De Morgan found out that it is possible to change a + sign to a sign and make or break a bar. See the 2 examples below:
"Make/break the bar and change the sign."
