The total number of prime implicants of the function 𝑓(𝑀, π‘₯, 𝑦, 𝑧) = βˆ‘(0,…

2015

The total number of prime implicants of the function 𝑓(𝑀, π‘₯, 𝑦, 𝑧) = βˆ‘(0, 2, 4, 5, 6, 10) is _______.

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Correct answer: 3

Approach: use a Karnaugh map to find maximal groups (prime implicants).

  • Place 1s at minterms 0, 2, 4, 5, 6, 10.

  • A 2Γ—2 block covering minterms 0, 2, 4, 6 (rows with w = 0 and columns with z = 0) is possible, giving the implicant w' z'.

  • Pair minterms 4 and 5 (0100 and 0101) to get the implicant w' x y'.

  • Pair minterms 2 and 10 (0010 and 1010) to get the implicant x' y z'.

These three are maximal groups (prime implicants) and together cover all given minterms.

Answer: total number of prime implicants = 3.

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