Following is the K-map of a Boolean function of five variables P, Q, R, S and X. The minimum sum-of-product (SOP) expression for the function is 
To determine the minimum Sum-of-Products (SOP) expression for the given Boolean function, we'll analyze each K-map based on the different values of \(X\).
Step 1: Analyze for \(X = 0\)
- Group the ones in the K-map (X=0):
- The cell at coordinates (PQ=01, RS=01) gives a term: \(\bar{P}QRS\bar{X}\).
- The cell at coordinates (PQ=11, RS=01) gives a term: \(PQRS\bar{X}\).
Step 2: Analyze for \(X = 1\)
- Group the ones in the K-map (X=1):
- The cell at coordinates (PQ=01, RS=00) gives a term: \(\bar{Q}\bar{R}\bar{S}X\).
- The cell at coordinates (PQ=11, RS=01) gives a term: \(QR\bar{S}X\).
Step 3: Combine the terms from \(X = 0\) and \(X = 1\)
- Simplify terms:
- From the analysis, notice how the expressions simplify to \(\bar{Q}S\bar{X} + Q\bar{S}X\) by combining like terms and considering the values X=0 and X=1 separately.
Conclusion: After analyzing and properly grouping and simplifying, the correct simplified SOP expression is \(\bar{Q}S\bar{X} + Q\bar{S}X\). This aligns with the provided correct answer choice:
$\bar{Q}S\bar{X} + Q\bar{S}X$
Important Questions from Karnaugh Maps
The minimized sum of products expression for f(a,b,c,d) = Ʃm(0,1,5,6,7,8,9) with don’t care Ʃm(10,11,12,13,14,15) is ___________.
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