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 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:
m0=A'*B'*C'
m1=A'*B'*C
m2=A'*B*C'
m3=A'*B*C
m4=A*B'*C'
m5=A*B'*C
m6=A*B*C'
m7=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   <- 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.

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