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Boolean Algebra and George Boole: An Introduction to Algebraic Logic - Prof. Gary Locklair, Study notes of Computer Science

An introduction to boolean algebra, a simplified form of algebra used in logic and electronics. The basics of boolean algebra, including variables, values, and operators such as not, or, and. It also explains the concept of a complete base and provides examples of how to create other boolean functions using combinations of a complete base. The document concludes with an assignment for students to demonstrate the completeness of the nor gate in creating all two-variable boolean functions.

Typology: Study notes

Pre 2010

Uploaded on 07/23/2009

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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

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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