Download presentation

Presentation is loading. Please wait.

Published byEvangeline Lynch Modified over 2 years ago

1
ITEC 352 Lecture 4 Boolean logic / Karnaugh Maps

2
K-Maps / Boolean logic Review Truth tables Conversion between Multiplexers

3
K-Maps / Boolean logic Outline Multiplexers Math –Karnaugh Maps –Minterm / Maxterm –Relationship to gates

4
K-Maps / Boolean logic Multiplexers Purpose? Construction using gates

5
K-Maps / Boolean logic Demultiplexer Only passes a 1 through if the input is 1

6
K-Maps / Boolean logic Combinatio n Why would you combine a multiplexer and a de-multiplexer?

7
K-Maps / Boolean logic Canonical forms A Boolean expression can be expressed in a number of ways. –E.g., S = X’+Y*Z can also be represented as S = X’ + X’ + Y*Z Hence,we use canonical forms (or normalized forms) that are unique in representing in expressions. –Note, they need not be minimal – they are just unique. Two popular canonical forms: –Sum of products and Product of sums.

8
K-Maps / Boolean logic Minterms Minterm: Boolean function that is 1 in only one row of the truth table. –Example: what are the minterms of function s. –S=X’ +Y*Z –Represent the sum (s) function using minterms.

9
K-Maps / Boolean logic Maxterms Maxterm: Boolean function that is 0 in only one row of the truth table. For example, the function: –Example maxterms for the sum function. –S=X’ +Y*Z Exercise: express F = X + Y' * Z as product of sums (in terms of maxterms)

10
K-Maps / Boolean logic Class exercise Implement a majority function: –Given three inputs, the functions equals 1, if the majority of inputs are 1’s else it is a 0. Steps: –(a) Draw the truth table. –(b) Write down the function in a canonicalized way. –(c) Draw the circuit.

11
K-Maps / Boolean logic K-Maps 2 Level Maximum

12
K-Maps / Boolean logic Constructio n Variant of a truth table –Grid format Allows you to see patterns quickly

13
K-Maps / Boolean logic Terms Implicant: a single minterm or group of minterms that can be combined together on the K-map Prime-implicants: Implicant that can not be combined with another one to remove a literal Essential prime implicants: prime implicant that includes a minterm not covered by any other prime implicant

14
K-Maps / Boolean logic Exercise Reduce the following Boolean expression using a Karnaugh Map: F = A’BC + AB’C + ABC + ABC’

15
K-Maps / Boolean logic Review A few mathematical terms –Minterm –Maxterm Visualization technique for Boolean expressions

Similar presentations

Presentation is loading. Please wait....

OK

CS1Q Computer Systems Lecture 7

CS1Q Computer Systems Lecture 7

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Laser video display ppt on ipad Ppt on media research center Ppt on chromosomes and chromatin related Ppt on creating brand equity Download ppt on oxidation and reduction in cellular Ppt on product design Ppt on password protected door lock system Ppt on online crime file management in java Ppt on programmable logic array Ppt on principles of object-oriented programming language