Fundamental Hardware Elements of Computers: Boolean algebra

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PAPER 2 - ⇑ Fundamentals of computer systems ⇑

← 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() 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.