Courses/Computer Science/CPSC 203/CPSC 203 2008Winter L03/CPSC 203 2008Winter L03 Lectures/Lecture 17

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  • House Keeping
    • Text Reading Databases -- Chapter 11 -- Pay particular attention to the sections: Data Storage, Managing Data , and Data Mining.
    • Text Reading -- Logic Associated Topics -- Chapter 9 (see pages below): Understand, Switches, Binary Numbers.
    • Assignment 1 Extension -- Now Due: Midnight March 24th.
      • We will review some Assignment 1 student examples from past semesters today
      • Additional Analysis Examples on BB: Under "Course Documents", "AnalysisExamples for Assignment 1".
    • NOTE: Tutorials the week of March 24tth will be devoted to TA's working with you on Group Projects
    • Time Boxed Assignments
      • Skillset for TBA3 is now up on Wiki
      • An example of output from TBA3 is on BB. Under "Course Documents", "TBA3 Word Example"


Lecture 17

Last class we introduced the basic operators of boolean logic, and their associated truth tables. We linked the back to Set Theory using Venn diagrams. Today, we will link forward the idea of a truth table to its realization as a circuit, i.e. a small machine that carries out the logic in a truth table. With these basics, we will then explore the structure of logic a little, by examining (a) how one can break a set of statements down to their logical form in a truth table and (b) what a more complex logic might look like which had three states" True, False, Uncertain (aka 3-valued logic).


OBJECTIVES:

  • You will be introduced to the basic types of circuits (that go into the building of computers).
  • Using truth tables and circuits you should be able to make very simple inferences.


Glossary

  • Logic Gate -- Performs a logic gate on one or more inputs, and produces a single logical output.
  • Digital Circuit -- Realization of one or more logic gates as a n electronic circuit.
  • Boolean Logic
  • Terms of Boolean Logic and Types of Circuits
    • AND
    • OR
    • NOT
    • XOR
    • Logical Implication; If X, Then Y; X-->Y

In Class Demonstrations

  • Working Through a slightly more complex truth table
  • Working Through a set of statements to their truth table
  • Working out the truth table for 3 valued logic.


The terms of Boolean Logic were illustrated by their respective Truth Tables. See also Wikipedia: http://en.wikipedia.org/wiki/Truth_table (note that in class we used 1 where they use "T", and we used 0 where they use "F"). Truth table values were then related to Logic gates: http://en.wikipedia.org/wiki/Logic_gates. Finally, logic gates were combined to build more complex circuit diagrams : http://en.wikipedia.org/wiki/Logic_gates.

For more on Boolean Logic please see: http://en.wikipedia.org/wiki/Boolean_Logic

A Computer Science oriented summary of Boolean logic is at: http://en.wikipedia.org/wiki/Boolean_logic

TEXT READINGS

TIA 4th Edn: Chapter 9 pp 406- 431 TIA 3rd Edn: Chapter 9 pp 386 - 409

Resources

The primary resource for this lecture was:

  • Ones & Zeros -- Understanding Boolean Algebra, Digital Circuits and the Logic of Sets. 1998. By John R. Gregg

Supplementary References are:

  • Logic. A Very Short Introduction. 2000. By Graham Priest.
  • Logic Made Easy. How to Know When Language Decieves You. 2004. By Deborah J. Bennett.
  • Feynman Lectures on Computation. 1996. By Richard P. Feynman.
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