Lecture DLC Materials for EEE Digital Logic circuits class material

Lecture_6.pptx

1. Lecture 6 UEE3303 Digital Logic Circuits 1 Dr. V Thiyagarajan Associate Professor Department of Electrical and Electronics Engineering Sri Sivasubramaniya Nadar College of Engineering Chennai, Tamil Nadu, INDIA – 603 110

2. Quine-McCluskey Method (Tabulation Method) 2 The Quine-McCluskey method (also known as the tabulation method ) is a systematic and algorithmic technique used in digital logic design to minimize Boolean functions. It's especially useful for minimizing functions with more than 4 variables , where Karnaugh maps become cumbersome.

3. Quine-McCluskey Method (Tabulation Method) 3 Steps in Quine-McCluskey Method (for SOP - Sum of Products): 1. List the Minterms Write down the minterms (i.e., the decimal indices of the truth table where output is 1). Convert each minterm to binary with fixed-length equal to the number of variables. 2. Group Minterms by the Number of 1’s Place binary minterms into groups based on how many 1s they contain. 3. Combine Minterms to Eliminate One Variable Compare terms from adjacent groups. If two terms differ by only one bit , combine them by replacing the differing bit with a dash ( – ), indicating a don’t care . Mark the combined terms so you know they are not prime implicants. Repeat this process until no further combinations are possible.

4. Quine-McCluskey Method (Tabulation Method) 4 Steps in Quine-McCluskey Method (for SOP - Sum of Products): 4. Identify Prime Implicants The terms that were never combined are called Prime Implicants . 5. Create a Prime Implicant Chart Make a chart mapping prime implicants vs. minterms . Mark which minterms are covered by which prime implicants. 6. Select Essential Prime Implicants A minterm that is covered by only one prime implicant makes that implicant essential . Choose all essential prime implicants. 7. Cover Remaining Minterms Find the minimum combination of prime implicants to cover all the remaining minterms .

5. Example - 1 5  

6. Example - 1 6

7. Example - 1 7

8. Example - 1 8

9. Example - 2 9

10. Example - 3 10 Using Quine - Mclusky tabulation method, obtain the set of prime implicants for the function

11. Example - 3 11

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16. References Morris Mano. M, “Digital Logic and Computer Design”, Prentice Hall of India, 3rd Edition, 2005. Donald D. Givone , “Digital Principles and Design”, Tata McGraw Hill, 1st Edition, 2003. Tocci R.J., Neal S. Widmer, “Digital Systems: Principles and Applications”, Pearson Education Asia, 12th Edition, 2017 Donald P Leach, Albert Paul Malvino , Goutam Sha, “Digital Principles and Applications”, Tata McGraw Hill, 7th Edition, 2010. Thomas L Floyd, “Digital fundamentals”, Pearson Education Limited, 11th Edition, 2018. 16

17. 17 Thank You