bernie
Uploaded by
15 SLIDES
301 VIEWS
150LIKES

Understanding Boolean Logic, Karnaugh Maps, and Multiplexers

DESCRIPTION

This lecture provides a comprehensive overview of Boolean logic, focusing on Karnaugh Maps, truth tables, and the conversion processes involving multiplexers and demultiplexers. We explore canonical forms, minterms, and maxterms, emphasizing their unique representations in Boolean expressions. Practical exercises include implementing majority functions and reducing Boolean expressions using Karnaugh Maps. Key mathematical terms such as implicants, prime-implicants, and essential prime-implicants are also covered, making it an essential session for understanding digital logic design.

1 / 15

Download Presentation

Understanding Boolean Logic, Karnaugh Maps, and Multiplexers

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. ITEC 352 Lecture 4 Boolean logic / Karnaugh Maps

  2. Review • Truth tables • Conversion between • Multiplexers

  3. Outline • Multiplexers • Math • Karnaugh Maps • Minterm / Maxterm • Relationship to gates

  4. Multiplexers • Purpose? • Construction using gates

  5. Demultiplexer • Only passes a 1 through if the input is 1

  6. Combination • Why would you combine a multiplexer and a de-multiplexer?

  7. 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. 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. 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. 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 • 2 Level Maximum

  12. Construction • Variant of a truth table • Grid format • Allows you to see patterns quickly

  13. 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. Exercise • Reduce the following Boolean expression using a Karnaugh Map: • F = A’BC + AB’C + ABC + ABC’

  15. Review • A few mathematical terms • Minterm • Maxterm • Visualization technique for Boolean expressions

More Related