A minterm, or

product term, is a

term in a

logical equation where:

- 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

variables, there are 2

^{X} minterms. Because of this, we can number the minterms, and refer to them as m

_{y} where y is the specific minterm we are talking about:

In a function with three variables A, B, and C:

m_{0}=A'*B'*C'

m_{1}=A'*B'*C

m_{2}=A'*B*C'

m_{3}=A'*B*C

m_{4}=A*B'*C'

m_{5}=A*B'*C

m_{6}=A*B*C'

m_{7}=A*B*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 <- m_{1}
0 1 0|1 <- m_{2}
0 1 1|0
1 0 0|1 <- m_{4}
1 0 1|0
1 1 0|0
1 1 1|0

Has an equation: F=m_{1}+m_{2}+m_{4}

Note that m must always be lowercase. An uppercase 'M' represents a maxterm.