# Chapter 3 Logic Gates and Boolean Algebra

Chapter 3 Logic Gates and Boolean Algebra Part 1 http://tennis.ecs.umass.edu/ece221 Fall 2002 1 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 DeMorgans theorem

Using NAND or NOR to implement a circuit Alternate gate symbols vs. standard logic-gate symbols Active high & Active low http://tennis.ecs.umass.edu/ece221 Fall 2002 2 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. http://tennis.ecs.umass.edu/ece221 Fall 2002 3 3-2 Truth Tables How a logic circuits output depends on the logic levels

present at the inputs. http://tennis.ecs.umass.edu/ece221 Fall 2002 4 3-3 OR Operation with OR gates Truth Table and circuit symbol http://tennis.ecs.umass.edu/ece221

Fall 2002 5 3-3 symbol and truth table for a three-input OR gate http://tennis.ecs.umass.edu/ece221 Fall 2002 6 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 http://tennis.ecs.umass.edu/ece221 Fall 2002 7

Example of the use of an OR gate in an Alarm system http://tennis.ecs.umass.edu/ece221 Fall 2002 8 Example 2 http://tennis.ecs.umass.edu/ece221 Fall 2002

9 Example3 http://tennis.ecs.umass.edu/ece221 Fall 2002 10 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? http://tennis.ecs.umass.edu/ece221 Fall 2002 11

3-4 And Operation with And Gates Truth Table and Gate symbol http://tennis.ecs.umass.edu/ece221 Fall 2002 12 Truth Table and Symbol for a three-input AND gate

http://tennis.ecs.umass.edu/ece221 Fall 2002 13 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 circuits 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. http://tennis.ecs.umass.edu/ece221 Fall 2002 14

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