# Fundamental Hardware Elements of Computers: Boolean algebra

We have met gate logic and combinations of gates. Another way of representing gate logic is through boolean algebra, a way of algebraically representing logic gates. You should have already covered the symbols, below is a quick reminder:

Bitwise Operator | NOT() | AND(.) | OR(+) | XOR() | NAND() | NOR() |
---|---|---|---|---|---|---|

Description | invert input | where exactly two 1s | where one or more 1s | where exactly one 1 | where less than two 1s | where exactly two 0s |

For the exam you might have:

- to convert logic gates into boolean algebra,
- build logic gate combinations from boolean algebra,
- simplify boolean algebra.

For example, in the exam it may ask you what is the boolean algebra for A or B?

The answer to this is A + B.

In the exam the question will most likely be harder to solve so you should learn how to combine all these into what you want to represent.