The Boolean SOP expression obtained from the truth table is:a)ABC+ABCb)ABC+ABCc)ABC+ABCd)ABC+ABCCorrect answer is option 'C'. Can you explain this answer? - EduRev Electronics and Communication Engineering (ECE) Question

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The Boolean SOP expression obtained from the truth table is:

a)
ABC'+A'BC
b)
AB'C+ABC'
c)
A'B'C+ABC'
d)
A'BC'+AB'C

Correct answer is option 'C'. Can you explain this answer?

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Most Upvoted Answer

The Boolean SOP expression obtained from the truth table is:a)ABC+ABCb...

We can minimize the Boolean expression/truth table of ‘n’ variable using a K-map in which 2ⁿ cells are present.
Steps to solve expression using K-map:

Select the K-map according to the number of variables (Cells = 2ⁿ)
Identify maxterm or minterm as given as per the problem.
For SOP, put 1’s in blocks of K-map respective to the minterms.
For POS, put 0’s in blocks of K-map respective to the max terms.
To minimize, make rectangular groups containing total terms in power of two (like 1, 2, 4, 8..).
From the groups made in step-5, find the product terms & add them for SOP form.

Calculation:
The truth table given is:

The 3 – variable K-map corresponding to the given truth table is drawn with 2³ = 8 (cells) as shown:

By making a group of 1’s,
Output (X) = A̅ B̅ C + A B C̅

Answered by Gate Gurus · View profile

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