Sum Of Products

A sum of products is a Boolean algebra expression of three levels:

1. Literals. This is the lowest level.
2. Either:
   • an and function, or nested and functions, with arguments taken from level 1, or
   • a literal from level 1.
3. Either:
   • an or function, or nested or functions, with arguments taken from level 2, or
   • an expression from level 2.
   This is the highest level.

This gives us a structure of or function(s) where the arguments are and function(s) where the arguments are literals. Any functions with only one input are replaced by their inputs. Logicians would say that the sum of products is in disjunctive normal form.

Example

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

References

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.