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

Fall 2002

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**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

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**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

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**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

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

Truth Table and circuit symbol Fall 2002

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

Fall 2002

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**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

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

Fall 2002

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

Example 2 Fall 2002

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

Example3 Fall 2002

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**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

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

Truth Table and Gate symbol Fall 2002

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

Fall 2002

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**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

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ACOE1611 Combinational Logic Circuits Reference: M. Mano, C. Kime, “Logic and Computer Design Fundamentals”, Chapter 2.

ACOE1611 Combinational Logic Circuits Reference: M. Mano, C. Kime, “Logic and Computer Design Fundamentals”, Chapter 2.

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