Anthony Catalano - EEWeb

TECHNICAL ARTICLE
Figure 1
There are three sets of rules that I
use to help break down Boolean
into more simple logic:
1. Break (or make) the line –
change the sign (DeMorgan’s
Theorem)
If you have a simple logic gate like
the NAND gate, then you write:
What you will find is that if you were
to invert (NOT) the logic levels of A
and B to get the same logic result
you would OR the inverted A and
B lines. By breaking the line above
the symbol and changing the sign,
it keeps the logic true:
2. Disappearing gates
When a gate has fixed inputs say at
logic ‘1’ or ‘0’, then the output also
becomes fixed. That’s because you
are restricting the combination of
outputs available. So the following
allows you to remove gates
completely from the circuit and
replace them with either a fixed
logic level or carry the logic signal
forward.
3. Adding fixed logic levels
This allows for making a logic gate
have more than n inputs. By adding
a fixed logic ‘1’ or ‘0’ input, then
that function of the gate remains
the same. However, it allows for
simplification of two gates with
common inputs (explained in
example at the end).
4. The “because it works” rule
These can be explained, but last
time I tried it took ages! So, like
the lecturers and teachers that
introduced me to Boolean, I’ll say
“just write these down because they
work.”
(And also to say this post would
become very long!)
The following is an example of
breaking down the logic into its
simplest form:
Consider the second and third
terms—the A.B is common to both.
Now imagine that the third term
also has a third input. This would—
for the AND gate to work—have to
be at logic ‘1’ as explained in my
third set of rules. This allows you to
combine the Boolean together into:
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