Consider a Boolean function f(w,x,y,z) such that f(w,0,0,z)=1, f(1,x,1,z)=x+z, f(w,1,y,z)=wz+y. The

Q: What is GATE-CS?

GATE-CS is a competitive examination conducted in India. This question is from the 2021 GATE-CS Digital Logic paper.

Q: How can I prepare for GATE-CS Digital Logic?

To prepare for GATE-CS Digital Logic, practice previous year questions (PYQs), understand concepts thoroughly, and solve mock tests regularly. This 2021 question covers Minimization (K-Map, Quine-McCluskey) topic.

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This GATE-CS 2021 Digital Logic question has a hard difficulty level and is marked as an important question.

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You can find more GATE-CS previous year questions on AspirantMitraa. Browse by subject, topic, year, and difficulty level to practice effectively.

Question

Consider a Boolean function f(w,x,y,z) such that f(w,0,0,z)=1, f(1,x,1,z)=x+z, f(w,1,y,z)=wz+y. The number of literals in the minimum sum-of-products expression of f is ___

Accepted Answer

Answer: 6Concept -- K-map Minimization with Partial Specification (from Morris Mano, Digital Design):From the given partial specifications, determine the complete truth table of f for all 16 minterms of (w,x,y,z), then minimize.f(w,0,0,z) = 1 for all w,z: minterms where x=0,y=0 -- that's (0,0,0,0)=m0, (0,0,0,1)=m1, (1,0,0,0)=m8, (1,0,0,1)=m9 are all 1.f(1,x,1,z) = x+z for x,z in {0,1}: w=1,y=1 means minterms m10(1010),m11(1011),m14(1110),m15(1111). f=x+z: m10(x=0,z=0)=0, m11(x=0,z=1)=1, m14(x=1,z=0)=1, m15(x=1,z=1)=1.f(w,1,y,z) = wz+y for w,y,z: x=1 minterms. f=wz+y.Filling all 16 minterms and applying K-map minimization yields a minimum SOP with 6 literals. Official answer: 6.

Consider a Boolean function f(w,x,y,z) such that f(w,0,0,z)=1, f(1,x,1,z)=x+z, f(w,1,y,z)=wz+y. The number of literals in the minimum sum-of-products expression of f is ___

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Consider a Boolean function f(w,x,y,z) such that f(w,0,0,z)=1, f(1,x,1,z)=x+z, f(w,1,y,z)=wz+y. The number of literals in the minimum sum-of-products expression of f is ___

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More Questions from Minimization (K-Map, Quine-McCluskey)

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