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(${\overline {A}}$)	AND(.)	OR(+)	XOR($\oplus$)	NAND(${\overline {A.B}}$)	NOR(${\overline {A+B}}$)
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.