Chapter 5

Karnaugh Map and Minimization Procedures

Ch05L4---"Digital Principles and Design", Raj Kamal, Pearson Education, 2006 2

Lesson 4

COMPUTER BASED MINIMIZATION – QUINE-

McCLUSKEY METHOD

Ch05L4---"Digital Principles and Design", Raj Kamal, Pearson Education, 2006 3

Step1 for is an exemplary expression

1. Write the expression for a Boolean function Y in terms of the product term. Y = Σ m (1, 3, 5, 6, 7, 10, 14, 15) = A. B. C. D + A. B.C.D + A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D

Ch05L4---"Digital Principles and Design", Raj Kamal, Pearson Education, 2006 4

Step 2a

• Let an index represent the number of 1s in a SOP term for Y. List all the term with index = 0 in one list, index = 1 in next list, index = 2 in next list, index = 4 in the next list and so on. For the four variable case, the maximum value of index = 4 and the indices are 0, 1, 2, 3 and 4.

Ch05L4---"Digital Principles and Design", Raj Kamal, Pearson Education, 2006 5

Step 2b

• Separate each list by underlining at the end of the list. Column 1 of a table shows the five lists for the example under description. There are four underlines in the four cells to separate five lists. There is no term in the list with index 0

Ch05L4---"Digital Principles and Design", Raj Kamal, Pearson Education, 2006 6

Step 2b

• Separate each list by underlining at the end of the list. Column 1 of a table shows the five lists for the example under description. There are four underlines in the four cells to separate five lists. There is no term in the list with index 0

Ch05L4---"Digital Principles and Design", Raj Kamal, Pearson Education, 2006 7

Step 2c

• Start from index 0 and find a pair of mini term in the corresponding list and next list with index =1. Index 0 list is empty. Therefore, switch to step 4 with no action.

• : Start from index 1 and find a pair of mini term in the corresponding list and next list with index =2.

Ch05L4---"Digital Principles and Design", Raj Kamal, Pearson Education, 2006 8

Step 2d

• Start from index 2 and find a pair of mini term in the corresponding list and next list with index = 3. The pair is the one, which satisfies the X.Y + X. Y = X, where Y is a single variable and Y is a single variable or a multivariable product term. Indices 2 and 3 lists are not empty. Therefore, the action is to be for finding the pairs after comparisons.

Ch05L4---"Digital Principles and Design", Raj Kamal, Pearson Education, 2006 9

Step 3

• Start from index 3 and find a pair of mini term in the corresponding list and next list with index = 4. The pair is the one, which satisfies the X.Y + X. Y = X, where Y is a single variable and Y is a single variable or a multivariable product term. Indices 3 and 4 lists are not empty.

Ch05L4---"Digital Principles and Design", Raj Kamal, Pearson Education, 2006 10

Step4

• Continue the above till no new list creates• Read Text for the details• Get the result = Σ m (1, 3, 5, 6, 7, 10, 14,

15) = Σ m (6, 10) =A. C. D + A..D + B.C

Ch05L4---"Digital Principles and Design", Raj Kamal, Pearson Education, 2006 11

Summary

Ch05L4---"Digital Principles and Design", Raj Kamal, Pearson Education, 2006 12

We learnt QUINE-McCLUSKEY method of finding prime implicants of a Boolean expression.

Ch05L4---"Digital Principles and Design", Raj Kamal, Pearson Education, 2006 13

End of Lesson 4

COMPUTER BASED MINIMIZATION – QUINE-

McCLUSKEY METHOD

Ch05L4---"Digital Principles and Design", Raj Kamal, Pearson Education, 2006 14

THANK YOU