A minterm, or product term
, is a term
in a logical equation
- Every variable that is present in the function is present in the term.
- All of these variables are represented as being either direct or complemented.
- All of the variables are AND'd together.
For a function with X variable
s, there are 2X
minterms. Because of this, we can number the minterms, and refer to them as my
where y is the specific minterm we are talking about:
In a function with three variables A, B, and C:
Notice the pattern of complements.
Once we have established what each minterm is, we can form a canonical equation in sum of products form by looking at a truth table for the function we wish to implement, and then ORing together all of minterms, which, when input to the system, result in a '1' as an output. So a function F with a truth table:
A B C|F
0 0 0|0
0 0 1|1 <- m1
0 1 0|1 <- m2
0 1 1|0
1 0 0|1 <- m4
1 0 1|0
1 1 0|0
1 1 1|0
Has an equation: F=m1+m2+m4
Note that m must always be lowercase. An uppercase 'M' represents a maxterm.