Digital logic questions on GATE (the Graduate Aptitude Test in Engineering) tend to follow a distinct pattern worth preparing for specifically: rather than just asking for a minimized expression, they often ask for a specific number derived from it — the total literal count, the number of essential prime implicants, or whether a unique minimal solution even exists. The two problems below are original, written in that style and fully verified — not reproduced from any actual past paper — to practice exactly that question format.
Question style 1: "What is the minimum number of literals?"
For F(A,B,C,D) = Σm(0,1,2,5,6,7,8,9,10,14), how many literals appear in the minimal SOP expression?
Working: Minimizing gives F = B′C′ + CD′ + A′BD — three terms with 2, 2, and 3 literals respectively.
A common wrong answer here comes from assuming all three terms are "essential" in the strict sense and stopping the check early — in fact, only B′C′ and CD′ are essential; A′BD is selected to complete the cover for the two minterms (5 and 7) that essential extraction alone doesn't reach. Getting the right literal count doesn't require knowing that distinction, but getting a follow-up question about which terms are essential does — see Essential vs. Non-Essential Prime Implicants.
Question style 2: "How many essential prime implicants does this function have?"
For F(A,B,C,D) = Σm(2,4,5,6,10,11,13,15), how many essential prime implicants exist?
Working: Building the full prime implicant chart finds 8 total prime implicants, each covering exactly 2 minterms, with every minterm covered by exactly 2 of them.
This is deliberately the trickiest version of this question style — a fully cyclic chart, verified and worked through in complete detail in Petrick's Method: Why Essential Prime Implicants Aren't Always Enough. A rushed answer of "some number greater than zero" is the single most common wrong answer to this exact question shape, because most practice problems (like question style 1 above) do have at least one essential PI, which trains the wrong reflex for the rarer cyclic case.
The pattern worth internalizing
Both examples above ask for a number, not an expression — which means the actual skill being tested is building the complete prime implicant chart correctly, not just producing a correct-looking simplified answer. Practicing the full chart-building process (not just pattern-matching to a plausible final expression) is what these question styles actually reward.
Verify the full prime implicant breakdown for either example directly: enter Σm(0,1,2,5,6,7,8,9,10,14) or Σm(2,4,5,6,10,11,13,15) into the 4-variable solver and check its Prime Implicant Analysis panel against the answers above.