A product of sums is a Boolean algebra expression of three levels:

- Literals. This is the lowest level.
- Either:
- an
`or`

function, or nested`or`

functions, with arguments taken from level 1, or - a literal from level 1.

- an
- Either:
- an
`and`

function, or nested`and`

functions, with arguments taken from level 2, or - an expression from level 2.

- an

This gives us a structure of `and`

function(s) where the arguments are `or`

function(s) where the arguments are literals.
Any functions with only one input are replaced by their inputs.
Logicians would say that the product of sums is in conjunctive normal form.

`(A or B) and (not(B) or C) and (A or C)`

`A and B`

`A or B`

`A`

Mano, M. Morris, and Kime, Charles R. *Logic and Computer Design Fundamentals. 2nd Edition.* Prentice Hall, 2000.

Kleitz, W. *Digital Microprocessor Fundamentals. 3rd Edition.* Prentice Hall, 2000.

Copyright © 2014 Barry Watson. All rights reserved.