-
In a minterm, each variable,
X, Y or Z appears once, either as the variable itself or as the inverse.
-
Each minterm corresponds
to exactly one entry (row!) in the truth table.
Implications of the two points above are that you can build any Boolean
function at all by building it up from minterms. There is no qualification
to this statement. Truly any Boolean function can be constructed
using minterms, and the construction process is simple.
To build any Boolean function from minterms do the following.
-
Get a truth table for
the function. Be sure that all possible combinations of variables
and inverses are accounted for.
-
For each entry of the
truth table for which the function takes on a value of 1,
determine the corresponding minterm expression remembering that every variable
of its inverse will appear in every minterm.
-
OR
all the minterms from the second step together.
We can sum up this conclusion with the following:
An
Example Using Minterms
To illustrate the use of minterms to get an electrical implementation of
a logic circuit, consider this problem. Three young graduates have
formed a company. The three graduates, Alisha, Ben and Corey have
a system to minimize friction. For all minor decisions they want
to use a circuit that will determine when a majority of the three of them
has voted for a proposal. Essentially, they want a box with three
inputs that will produce a 1
at the output whenever two or more of the inputs are 1.
The solution process starts by getting the truth table. That's shown
below. Notice that there are four 1
entries
in the table. Those 1s
occur when two people vote Yes
together or when all three vote together.
|
A
|
B
|
C
|
V
|
|
0
|
0
|
0
|
0
|
|
0
|
0
|
1
|
0
|
|
0
|
1
|
0
|
0
|
|
0
|
1
|
1
|
1
|
|
1
|
0
|
0
|
0
|
|
1
|
0
|
1
|
1
|
|
1
|
1
|
0
|
1
|
|
1
|
1
|
1
|
1
|
After getting the truth table, the next step is to identify the minterms.
That's shown below where the minterms are to the right of the corresponding
entries in the truth table. There are four 1
entries in the truth table and four corresponding minterm expressions.
|
A
|
B
|
C
|
V
|
|
0
|
0
|
0
|
0
|
|
0
|
0
|
1
|
0
|
|
0
|
1
|
0
|
0
|
|
0
|
1
|
1
|
|
|
1
|
0
|
0
|
0
|
|
1
|
0
|
1
|
|
|
1
|
1
|
0
|
|
|
1
|
1
|
1
|
|
|
