Russ Croman - EEWeb

TECHNICAL ARTICLE
B
Figure 2
A
0
0 1
0 1
1 1 1
Then, like a truth table, you fill in
when the output will be a logical 1
or 0. If we were to write down the
Boolean Algebra for this in order to
represent each square with a 1 in it,
we would get:
F = !A.B+A.!B+A.B
This is messy because there are
four gates and we know we only
need one. Using Boolean Algebra
would break this down to A+B. So
how can the K-Map do the same?
The answer is: loops! The idea
is to loop together like terms. For
example, we can loop together !B.A
with B.A. This loop then represents
the common term in the loop,
ignoring any element that changes.
Because B changes this loop simply
represents A.
B
Figure 3
A
0
0 1
0 1
1 1 1
The same can then be done with
!A.B and A.B to give a loop that is
equal to B. We now have two loops,
A and B, so the final solution which
we know to be true is: A+B
Another example is as follows:
B
Figure 4
A
0
0 1
1 1
1 0 1
With the loops in place, we can
quickly see that the answer is A+!B.
What makes K-Maps so useful is that
you can quickly see the answers.
Now before we move on to bigger
K-Maps we need some ground
rules to follow!
• Loops can only go up or down –
NOT diagonally.
• Loops contain an EVEN number
of terms, however, looping one
item is allowed.
• - So, only: 1, 2, 4 or 8 terms are
allowed per loop!
• Loops only wrap common
terms.
• Loops must always be square
or rectangle – no funny blob
shapes!
• Terms in the loops are AND’ed
together.
• All Loops are then OR’ed
together for the final result.
These aren’t the difficult rules you
would expect but this is basically all
you need to know!
So lets jump past three inputs to
four inputs as you will hopefully
figure out how to do three from
this example. My truth table is as
follows:
Figure 6
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D
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
Figure 5
C
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
B
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
BA
00
DC
01
00 0 1
01
11
10
1
0
1 1
0 0
A
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
F
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
1
11 10
1 0
0 1
1 1
0 0
TECHNICAL ARTICLE