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