Fundamental Hardware Elements of Computers: Boolean algebra

 ← Building circuits Boolean algebra Simplifying boolean equations →

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