16 October Day 15
Chapter 3
Background on George Boole
What is an Algebra?
Boolean Algebra
variables/values {0,1}
simpler than regular algebra; each variable could have an
infinite number of values!
operators (functions)
1. not
2. or
3. and
4. etc
review truth table representation, logic symbol, and notational
symbol
A complete base is a subset of the 16 possible two-variable functions
(table on page 16) which can be used to perform any (and all) other
Boolean functions. In other words, using just 3 (say) functions, I can
create the other 12 functions by using “combinations” of the three
available in the complete base.
Ex: (And, Or, Not) is a complete base. Using combinations, I can make
any other Boolean function. A (Nand) function can be made using a
(And) and a (Not), for example.
Ex: (Nand) is complete by itself. Demo by creating (And), (Or), and
(Not) using just (Nand) gates.
--- Electronics WorkBench demo---
ASSIGN7 – Problem 1. How? Either by showing that (Nor) can create
all other (15) two-variable Boolean functions, or by showing that (Nor)
can create (Or), (And), and (Not) functions from just (Nor) gates.
CSC 490 Course Notes and Outline, © Dr. Gary Locklair, Fall 2006
