Brief Introduction to Boolean Algebra - PowerPoint PPT Presentation

1 / 5
About This Presentation
Title:

Brief Introduction to Boolean Algebra

Description:

Manufacturing is simplified with NAND/NOR. NAND/NOR avoid problem ... Converting between AND/OR circuits and NAND/NOR circuits is easy with Boolean Algebra. ... – PowerPoint PPT presentation

Number of Views:156
Avg rating:3.0/5.0
Slides: 6
Provided by: csiS7
Category:

less

Transcript and Presenter's Notes

Title: Brief Introduction to Boolean Algebra


1
Brief Introduction to Boolean Algebra
  • We can use transistors to build AND, OR, NAND,
    NOR, and Invertors
  • Manufacturing is simplified with NAND/NOR
  • NAND/NOR avoid problem with transistor
    bleed-through
  • Converting between AND/OR circuits and NAND/NOR
    circuits is easy with Boolean Algebra.
  • (named for mathematician George Boole)
  • Boolean Variable can be in just two states 0
    or 1
  • Represent Boolean Variables with letters

2
Example
  • Two inputs (Boolean variables) A and B are ANDed
    together.
  • The AND operation is represented in a Boolean
    equation with the multiplication symbol
    (overloading of operator!)
  • (The OR operation is represented with the
    addition symbol )
  • A AND B can be represented as AB
  • A OR B can be represented as A B

A
B
3
DeMorgans Theorem
  • On of the most useful principles in boolean
    algebra is DeMorgans Theorem, which allows one
    to switch between ANDs and NORs and OR and NAND
  • NOT terms or Inverted terms are represented with
    a line over the terms
  • AB A B
  • A B AB

4
  • To convert AB into a form that can be
    implemented using a NAND gate follow these steps
  • 1. Double Complement the term AB AB
  • 2. Use DeMorgans to distribute one of the
    complements
  • AB A B
  • The equation is now a NAND of the complemented
    inputs.

5
  • A B OR A B AAND B ANAND B
  • 0 0 0 1 1 1 0
  • 0 1 1 1 0 0 1
  • 1 0 1 0 1 0 1
  • 1 1 0 0 0 1
  • Note that the third and last columns are
    equivalent.
  • Complements of input values are easy to get, and
    may already be available.
Write a Comment
User Comments (0)
About PowerShow.com