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

Info iconThis preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon
ENGIN112 L5: Boolean Algebra September 12, 2003 COSC 232 Digital Logic Boolean Algebra Prepared by: Russell Tessier Edited by: Michael Jack
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 2
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
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 4
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
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 6
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
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 8
ENGIN112 L5: Boolean Algebra September 12, 2003 Consider three-input gates 3 Input OR Gate
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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:
Background image of page 10
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
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 12
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 35

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

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online