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What is the minimal from of Karnaugh map shown below? (Assume that x denotes a don't care term)

What is the minimal from of Karnaugh map shown below? (Assume that x denotes a don't care term) Correct Answer b̅ d̅ + b̅ c̅ 

The correct answer is b̅ d̅ + b̅ c̅ .

Key Points

 

  • There are two prime implicants in the following K-Map-

Additional Information

  • In many digital circuits and practical problems, we need to find expression with minimum variables.
  • We can minimize Boolean expressions of 3, 4 variables very easily using K-map without using any Boolean algebra theorems.
  • K-map can take two forms Sum of Product (SOP) and Product of Sum (POS) according to the need of the problem.
  • K-map is a table-like representation but it gives more information than TRUTH TABLE.
  • We fill the grid of K-map with 0’s and 1’s then solve it by making groups.
  • Steps to solve expression using K-map-In many digital circuits and practical problems,
    • We need to find expression with minimum variables.
  • We can minimize Boolean expressions of 3, 4 variables very easily using K-map without using any Boolean algebra theorems.
  • K-map can take two forms Sum of Product (SOP) and Product of Sum (POS) according to the need of the problem.
  • K-map is a table-like representation but it gives more information than TRUTH TABLE.
  • We fill the grid of K-map with 0’s and 1’s then solve it by making groups.
  • Select K-map according to the number of variables
    • Identify minterms or max terms as given in the problem.
    • For SOP put 1’s in blocks of K-map respective to the minterms (0’s elsewhere).
    • For POS put 0’s in blocks of K-map respective to the max terms(1’s elsewhere).
    • Make rectangular groups containing total terms in the power of two like 2,4,8 ..(except 1) and try to cover as many elements as you can in one group.
    • From the groups made in step 5 find the product terms and sum them up for SOP form.

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