Download presentation

Published byIan Burkley Modified over 4 years ago

1
**Chapter 3 Logic Gates and Boolean Algebra – Part 1**

Fall 2002

2
**http://tennis.ecs.umass.edu/ece221 Fall 2002**

Objectives Three basic logic operations: AND, OR, NOT Operation of logic circuits and construction of truth tables Timing diagrams for the various logic-circuit gates Boolean expression for the logic circuits Implement logic circuits using AND, OR, NOT Simplify logic expressions DeMorgan’s theorem Using NAND or NOR to implement a circuit Alternate gate symbols vs. standard logic-gate symbols Active high & Active low Fall 2002

3
**3-1 Boolean Constants and variables**

Boolean constants and variables are allowed to have only two possible values, 0 or 1. Boolean 0 and 1 do not represent actual numbers but instead represent the state of a voltage variable, or what is called its logic level. 0/1 and Low/High are used most of the time. Three Logic operations: AND, OR, NOT Logic Gates Digital circuits constructed from diodes, transistors, and resistors whose output is the result of a basic logic operation(OR, AND, NOT) performed on the inputs. Fall 2002

4
**http://tennis.ecs.umass.edu/ece221 Fall 2002**

3-2 Truth Tables How a logic circuit’s output depends on the logic levels present at the inputs. Fall 2002

5
**3-3 OR Operation with OR gates**

Truth Table and circuit symbol Fall 2002

6
**3-3 symbol and truth table for a three-input OR gate**

Fall 2002

7
**Summary of OR operation**

Produce a result of 1 whenever any input is 1. Otherwise 0. An OR gate is a logic circuit that performs an OR operation on the circuit's input The expression x=A+B is read as “x equals A OR B” Fall 2002

8
**Example of the use of an OR gate in an Alarm system**

Fall 2002

9
**http://tennis.ecs.umass.edu/ece221 Fall 2002**

Example 2 Fall 2002

10
**http://tennis.ecs.umass.edu/ece221 Fall 2002**

Example3 Fall 2002

11
**http://tennis.ecs.umass.edu/ece221 Fall 2002**

Review Questions What is the only set of input conditions that will produce a LOW output for any OR gate? Write the Boolean expression for a six-input OR gate If the A input in previous example is permanently kept at the 1 level, what will the resultant output waveform be? Fall 2002

12
**3-4 And Operation with And Gates**

Truth Table and Gate symbol Fall 2002

13
**Truth Table and Symbol for a three-input AND gate**

Fall 2002

14
**Summary of the AND operation**

The AND operation is performed the same as ordinary multiplication of 1s and 0s. An AND gate is a logic circuit that performs the AND operation on the circuit’s inputs. An AND gate output will be 1 only for the case when all inputs are 1; for all other cases the output will be 0. The expression x=AB is read as “x equals A AND B.” Fall 2002

Similar presentations

OK

Lecture 4 Introduction to Boolean Algebra. Binary Operators In the following descriptions, we will let A and B be Boolean variables and define a set of.

Lecture 4 Introduction to Boolean Algebra. Binary Operators In the following descriptions, we will let A and B be Boolean variables and define a set of.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google