Minimize the following Boolean function represented in Sum-of-Products (SOP) form:
$F(A, B, C, D) = \sum m(0, 2, 5, 7, 8, 10, 13, 15)$
Which of the following is the simplified Boolean expression?
Asked by Rahul_Mehta | Textbook Reference: Mano Digital Design
[Variation 9 Explanation] Using a 4-variable K-map: - Group 1: minterms $5, 7, 13, 15 \implies$ simplified to **BD**. - Group 2: minterms $0, 2, 8, 10 \implies$ simplified to **B'D'**. Simplified expression is $F = BD + B'D'$. Option A is correct.
[Variation 9 Explanation] ### Alternative Approach / Shortcut Method We can also solve this problem by eliminating incorrect choices or utilizing shortcut relations. For a GATE candidate, speed is as important as accuracy. Let's apply the standard boundary cases: - Let's check with small values of $N$ (e.g. $N=1, 2, 3$). - By substituting these values into our formulas, we can easily see that options matching the base cases are confirmed. This alternative proof validates our selected consensus solution!
[Variation 9 Explanation] ### Critical Warnings & Common Student Pitfalls Many students make simple mistakes when solving this type of problem in the exam pressure: 1. **Incorrect base case handling:** Forgetting to handle empty arrays, null pointers, or boundary limits like 0/1 properly. 2. **Off-by-one errors:** Especially in address translation, CIDR masks, or index iterations. 3. **Mismatched units:** Mixing up bits vs bytes, or Hertz vs seconds. Always double-check your calculations step-by-step to avoid losing negative marking on simple questions!