A minterm is the smallest possible "1": a product term that is true for exactly one combination of the inputs.
To build one, take every variable once. Write the variable plain if it should be 1 on that row, primed if it should be 0. The AND of all those literals is 1 only when every literal is 1, which happens on one row and no other.
Minterms are numbered by their row. mᵢ is the minterm for row i, where i is the input pattern read as a binary number with the first variable as the MSB. With inputs A, B, C (weights 4, 2, 1):
m0=000=m5=101=m7=111=
Why they matter: OR together the minterms of the rows where a function is 1 and you get an expression that is always correct. That is the sum of minterms, and it's the starting point of every design. A decoder produces every minterm of its inputs, one per output line.
The partner idea is the maxterm, a sum term that is 0 on exactly one row.
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 0 |