Question

Can you Simplify X = A’B’CD’+A’BC’D+A’BCD+ABC’D+ABCD+AB’CD Using K Map [5 marks]

Answer 1

Simplifying the boolean algebra using K-maps :

Given boolean algebraic expression is :

A’B’CD’+A’BC’D+A’BCD+ABC’D+ABCD+AB’CD

Karnaugh Map :

Please look at the attachment given below

to find the K Map.

Simplified boolean algebraic expression using K map:

A'B'CD' + BD + ACD

Explanation :

• After mapping the values on the k-map based on each term in the given expression, map 2x2 or 2 sequences, if you find any.

• Once marked, check the grouped slot and find what are the variables that left unchanged.

• For example, if you take 2x2 slot, you can find that among A'B and AB, B remained same, among C'D and CD, D remained same. So, The group together results simplified expression BD.

• Similarly, if you have a look at AB and AB' in 2 grouped slot, A remained unchanged and so do CD. So, the group results ACD.

• As A'B'CD' remained alone, write it as it is and add all the results to get the final result. (Check once again if anything can be simplified further once you summedup the individual results).

There we get, A'B'CD' + BD + ACD and it can't be simplified any further.

Learn more :

• Maximum Number of Variables Used to Draw a K-Map .

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• K map for SR flipflop.

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