Combinational
logic  Basic Applications of Boolean Gates
Experiments with electronic gates

Logic
circuits
can be divided into
two
major sections:
combinational
logic and sequential
logic. The main difference
is that
the first type of
circuit logic doesn’t depend on time or
sequence of movements, and
the
second
type of logic does.
A clear example
to understand
this difference can be
illustrated by showing the two locks
below: 


Combinational Logic 
Sequential Logic 
The
lock on the left has four discs that can be rotated separately. When
the
notches are aligned, the metal hook is released. The only one condition
needed is
that the appropriate four notches are aligned, no matter if the left
disc is set
before the one on the right. The lock will open if you have the
correct
combination.
On the
contrary, the lock on the right has only one knob, and the combination
could be
3cw – 52ccw – 20cw. This means that one must first get to number 3
going
clockwise, then to 52 counterclockwise, and finally get to number 20
clockwise.
If you use the same numbers in different order, the lock won’t open.
This is a sequential
lock, a correct sequence is important.
Due to
its stability, reliability, low maintenance and ease at reading digital
displays, these days everything is going the digital way.
Logic
circuits can be simulated with the so called boolean or logic gates.
This is kind of Digital
Electronics 101...
Let’s
say that we’d like to find out the behavior of the following
combinational
circuit:
We can
create an mfile to effortlessly solve the logic circuit, like this:
function f =
combination(x)
%
x(1) = A
%
x(2) = B
%
x(3) = C
%
Symbol ~ is used for NOT gates
%
We have 4 logicAND gates
and1 =
~x(1) & ~x(2) & ~x(3);
and2 =
~x(1) & x(2) & ~x(3);
and3 =
~x(1) & ~x(2) & x(3);
and4 =
~x(1) & x(2) & x(3);
%
We have 1 logicOR gate
f = and1
 and2  and3  and4;
We can
test our function for this specific example of combinational logic:
%
These are all the possible combinations for 3 inputs
M = [ 0
0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1];
%
We give all the combinations, one at a time
for i = 1 :
8
comb_log(i) =
combination(M(i, :));
end
%
We display the results
comb_log
The
results are:
comb_log
= 1
1
1
1
0
0
0
0
If
you make some analysis using the DeMorgan laws, you can
conclude
that this function can also be simplified to F = not(A), and you can
visualize it from the results...
This
means that we have not only a MATrix LABoratory, but we've
got also a
circuit
logic simulator!
From 'Combinational Logic'
to home
From
'Combinational Logic' to 'Boolean Algebra'
