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Chapter 3 Logic Gates and Boolean Algebra – Part 1

Chapter 3 Logic Gates and Boolean Algebra – Part 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

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Chapter 3 Logic Gates and Boolean Algebra – Part 1

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

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

  4. 3-2 Truth Tables • How a logic circuit’s output depends on the logic levels present at the inputs. http://tennis.ecs.umass.edu/ece221 Fall 2002

  5. 3-3 OR Operation with OR gates • Truth Table and circuit symbol http://tennis.ecs.umass.edu/ece221 Fall 2002

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

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

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

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

  11. 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

  12. 3-4 And Operation with And Gates • Truth Table and Gate symbol http://tennis.ecs.umass.edu/ece221 Fall 2002

  13. Truth Table and Symbol for a three-input AND gate http://tennis.ecs.umass.edu/ece221 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.” http://tennis.ecs.umass.edu/ece221 Fall 2002

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