ece15_8__11_6

ece15_8__11_6 - Last time: Karnaugh Map Method to find...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
1 ECE 15A Fundamentals of Logic Design Lecture 8 Malgorzata Marek-Sadowska Electrical and Computer Engineering Department UCSB 2 Last time: Karnaugh Map Method to find minimum SOP Step 1: Choose an element of ON-set not already covered by an implicant Step 2: Find "maximal" groupings of 1's and X's adjacent to that element. Remember to consider top/bottom row, left/right column, and corner adjacencies. This forms prime implicants (always a power of 2 number of elements). Repeat Steps 1 and 2 to find all prime implicants Step 3: Revisit the 1's elements in the K-map. If covered by single prime implicant, it is essential , and participates in final cover. The 1's it covers do not need to be revisited Step 4: If there remain 1's not covered by essential prime implicants, then select the smallest number of prime implicants that cover the remaining 1's 3 Discussion Karnaugh maps are: Very effective for functions up to 6 variables Not useful for functions dependent on >6 variables K-maps depend on human’s visual ability to identify prime implicants K-maps are not helpful in developing CAD tools 4 2-level simplification approaches Algebraic simplification Not a systematic procedure Difficult to tell when the minimum expression has been found Hand methods K-maps Quine-McCluskey method (aka Tabular Method) Computer-aided tools High quality solutions for large functions ( more than 10 variables) Heuristic methods applied Espresso Exact solutions for unate function Shannon expansion 5 Quine-McCluskey method Tabular method to systematically find all prime implicants Can be programmed 6 Outline of the Quine-McCluskey Method 1. Produce a minterm expansion (canonical sum-of-products form) for a function F 2. Eliminate as many literals as possible by systematically applying XY + XY’ = X . 3. Use a prime implicant chart to select a minimum set of prime implicants that when ORed together produce F, and that contains a minimum number of literals.
Background image of page 1

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

View Full DocumentRight Arrow Icon
2 7 Determining Prime Implicants AB’CD’ + AB’CD = AB’C 1 0 1 0 + 1 0 1 1 = 1 0 1 - (The dash indicates a missing variable) A’BC’D + A’BCD’ 0 1 0 1 + 0 1 1 0 We can combine the minterms above because they differ by a single bit.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 6

ece15_8__11_6 - Last time: Karnaugh Map Method to find...

This preview shows document pages 1 - 3. Sign up to view the full document.

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