SOP and POS
SOP (Sum of Product)
Lecture notes: 04 Boolean algebra - Lecture, p.18
Features:
- Can count how many times the expression results to 1 by counting the number of parts or number of (+)
- Once one of the 'parts' is 1, the expression results to 1
Steps
- Find all the columns where the result is 1
- Get the 'part', when the variables is equal to 1
- Combine all of the parts together, by 'adding' (OR) together
Example
Truth table for A!C+B:
| A | B | C | A!C+B | Parts |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | - |
| 0 | 0 | 1 | 0 | - |
| 0 | 1 | 0 | 1 | !AB!C |
| 0 | 1 | 1 | 1 | !ABC |
| 1 | 0 | 0 | 1 | A!B!C |
| 1 | 0 | 1 | 0 | - |
| 1 | 1 | 0 | 1 | AB!C |
| 1 | 1 | 1 | 1 | ABC |
| SOP = Add up all the parts | ||||
| SOP = !AB!C+!ABC+A!B!C+AB!C+ABC | ||||
| If simplify ^, will end up with A!C+B |