L2 Boolean Algebra

# L2 Boolean Algebra - COSC 232 Digital Logic Boolean Algebra...

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ENGIN112 L5: Boolean Algebra September 12, 2003 COSC 232 Digital Logic Boolean Algebra Prepared by: Russell Tessier Edited by: Michael Jack

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ENGIN112 L5: Boolean Algebra September 12, 2003 Overview ° Logic functions with 1’s and 0’s Building digital circuitry ° Truth tables ° Logic symbols and waveforms ° Boolean algebra ° Properties of Boolean Algebra Reducing functions Transforming functions
ENGIN112 L5: Boolean Algebra September 12, 2003 Digital Systems ° Analysis problem: Determine binary outputs for each combination of inputs ° Design problem: Given a task, develop a circuit that accomplishes the task - Many possible implementations - Try to develop “best” circuit based on some criterion (size, power, performance, etc.) . . . . Logic Circuit Inputs Outputs

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ENGIN112 L5: Boolean Algebra September 12, 2003 Toll Booth Controller ° Consider the design of a toll booth controller ° Inputs: quarter, car sensor ° Outputs: gate lift signal, gate close signal ° If a driver pitches in a quarter, raise the gate. ° When the car has cleared the gate, close the gate. Logic Circuit \$.25 Car? Raise gate Close gate
ENGIN112 L5: Boolean Algebra September 12, 2003 Describing Circuit Functionality: Inverter ° The above circuit is an inverter. An input of 0 is inverted to a 1. An input of 1 is inverted to a 0. ° Basic logic functions have symbols. ° The same functionality can be represented with truth tables. Truth table completely specifies outputs for all input combinations. 0 1 1 0 Y A Input Output A Y Symbol Truth Table

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ENGIN112 L5: Boolean Algebra September 12, 2003 The AND Gate ° If the two input signals are asserted (high) the output is also asserted. Otherwise, the output will be deasserted (low). 1 1 1 0 0 1 0 1 0 0 0 0 Y B A A B Y Truth Table
ENGIN112 L5: Boolean Algebra September 12, 2003 The OR Gate ° If either of the two or both of the input signals are asserted, the output is asserted. 1 1 1 1 0 1 1 1 0 0 0 0 Y B A A B Y Truth Table

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ENGIN112 L5: Boolean Algebra September 12, 2003 Describing Circuit Functionality: Waveforms ° Waveforms provide another approach for representing functionality. ° Values are either high (logic 1) or low (logic 0). ° Can you create a truth table from the waveforms? 1 1 0 1 1 0 0 0 y x AND Gate
ENGIN112 L5: Boolean Algebra September 12, 2003 Consider three-input gates 3 Input OR Gate

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ENGIN112 L5: Boolean Algebra September 12, 2003 Ordering Boolean Functions ° How to interpret A + B C? Is it B C ORed with A ? Is it A ANDed with B C ? ° Order of precedence for Boolean algebra: AND before OR ° Note that parentheses are needed here:
ENGIN112 L5: Boolean Algebra September 12, 2003 Boolean Algebra ° A Boolean algebra is defined as a closed algebraic system containing a set K of two or more elements and two operators, ( ) and (+). ° Useful for identifying and

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L2 Boolean Algebra - COSC 232 Digital Logic Boolean Algebra...

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