Anthony Catalano - EEWeb

Illogical Logic
Part 1 - Boolean Algebra
Paul Clarke
Electronics Design Engineer
When it comes to logic, we know it’s all supposed to
make sense. For newcomers, it can also be very confusing
to wrap your head around these concepts. This is why I
have decided to do a short series on understanding the
illogical world of logic!
For the most part, understanding basic logic gates is easy
enough. They explain what they are clearly; an AND gate
just says the output is: logic ‘1,’ then input ‘x’ AND ‘y’ are
logic ‘1.’ If you’re not 100% on this and other logic gates,
then a quick read on Wikipedia will help set you straight.
What becomes confusing is that we use lots of logic gates
together, like in an FPGA. So, how do you work out what
you need and why do some people seem to use so few
gates for such complex tasks?
Boolean algebra is a way of explaining logic in a written
form without having to draw out all the logic gates. In
place of an AND gate, you simply write A.B (note the full
stop), and for the OR function you use the plus symbol (for
example: A+B). This means you can turn complex logic
into one written line of Boolean (Figure 1).
What’s shown in Figure 1 quickly becomes…
However, Boolean allows you to do things you cannot see
or work out from a logic circuit. Boolean allows you to
apply simple rules that will enable you to break down the
logic to simply the elements that matter.
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