| Boolean functions: minterms | |||||||||||||
| Consider a particular truth table with 3 inputs: | |||||||||||||
| row | x0 | x1 | x2 | z | |||||||||
| 0 | 0 | 0 | 0 | 0 | |||||||||
| 1 | 0 | 0 | 1 | 0 | |||||||||
| 2 | 0 | 1 | 0 | 0 | |||||||||
| 3 | 0 | 1 | 1 | 0 | |||||||||
| 4 | 1 | 0 | 0 | 0 | |||||||||
| 5 | 1 | 0 | 1 | 1 | x0\x1x2 == | x0 AND ~x1 AND x2 | |||||||
| 6 | 1 | 1 | 0 | 0 | |||||||||
| 7 | 1 | 1 | 1 | 0 | |||||||||
| Want to write a Boolean function for this truth table | |||||||||||||
| Definition: literal is either a Boolean variable (x) or its negation (\x); text uses overbar | |||||||||||||
| We need to write some expressions involving literals for the 3 inputs | |||||||||||||
| Minterm: a term containing exactly 1 instance of each variable, either itself | |||||||||||||
| or its complement. | |||||||||||||
| Example: in row 5, x0\x1x2 has the value 1. | |||||||||||||