minterm (idea)

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:
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.