Boolean algebra is a mathematical way to represent the logic that takes place inside the CPU, more specifically the ALU (arithmetic logic unit). Using a set of standard mathematical symbols to represent the logic that we wish to represent means that we can define logical equations in a much more simplified format then if we were using a logic circuit diagram.

In the table below you will see the symbols which are used to represent the different logic gates.

In this table we have used a dot to represent the AND gate, an addition sign to represent the OR gate, an over line to represent the NOT gate, and the addition sign surrounded by a circle to represent the eXclusive OR gate.

Now we are aware of these four main signs, we can combine them together to create much more complex boolean logic, remembering that we also need to take into consideration that brackets allow us to encapsulate the different sections. The only difference here is that when we want to use more complex gates such as NAND and NOR the line over the top of the inputs that symbolises the NOT gate is extended over both inputs.

Try this for yourself. For example, what would it look like if we were to write out the boolean expression below as Boolean algebra?

Q = A AND (B OR C) OR (B AND A)

### Answer

Q = A . (B + C) + (B . A)

Try this again with a slightly more complex boolean expression, but this time in reverse:

### Answer

Q = NOT (A OR B) AND (C XOR B)

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