A sum of products is an OR ("sum") of product terms, where each product is an AND of literals. Bars sit only on single letters. Examples: , , or a single product like .
These are not SOP: (a bracket inside a product) and (a bar over a product). Both can be converted, by multiplying out or by de morgans laws.
Why SOP is the standard shape:
- Any function can be written as an SOP. Take one minterm for each row where the output is 1 and OR them together.
- It is easy to compare terms side by side, which is what combining, absorption and consensus need.
- It maps straight onto hardware: one AND gate per term feeding one OR gate, a two-level circuit, which converts directly to NAND-NAND.
A minimal sop uses the fewest terms and then the fewest literals. Its mirror image, an AND of OR terms, is the product of sums.
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 1 |