| Boolean functions: sum of products | |||||||||||||
| What if more than one output in the truth table is 1? | |||||||||||||
| If m outputs are 1, we need m minterms. | |||||||||||||
| For each row with output 1, construct the minterm. | |||||||||||||
| Combine the minterms by OR operators. | |||||||||||||
| This is called the sum of products. | |||||||||||||
| Products: each minterm is the result of combining literals with AND | |||||||||||||
| Sum: represents combining minterms with OR | |||||||||||||
| Example: | |||||||||||||
| row | x0 | x1 | x2 | z | Minterms | ||||||||
| 0 | 0 | 0 | 0 | 0 | |||||||||
| 1 | 0 | 0 | 1 | 0 | |||||||||
| 2 | 0 | 1 | 0 | 1 | \x0x1\x2 | ||||||||
| 3 | 0 | 1 | 1 | 0 | |||||||||
| 4 | 1 | 0 | 0 | 0 | |||||||||
| 5 | 1 | 0 | 1 | 1 | x0\x1x2 | ||||||||
| 6 | 1 | 1 | 0 | 0 | |||||||||
| 7 | 1 | 1 | 1 | 1 | x0x1x2 | ||||||||
| Function: | z = \x0x1\x2 + x0\x1x2 + x0x1x2 | ||||||||||||