Digital Logic : Logic Functions and Minimisation GATE Previous Years Questions Solved

Ques 1: What is the equivalent Boolean expression in product-of-sums form for the Karnaugh map given below.

GATE 1996

(A) BD’ + B’D
(B) (B+C’+D)(B’+C+D’)
(C) (B+D)(B’+D’)
(D) (B+D’)(B’+D)


Solution: For POS Form, Consider 0 s and k-map is

Ques 2: Let * be defined as x*y= x’+y. Let z = x*y. Value of z*x is

GATE 1997

 (A) x +y

(B) x

(c) 0

(D) 1

Ans: (B)

Solution: z*x


=(x*y)’ + x

=(x’+y)’ + x

= x.y’ + x


Ques 3: Let f(x, y, z) = x’ + y’x + xz be a switching function. Which one of the following is valid?

GATE 1997

(A) y’z is a prime implicant of f
(B) xz is a minterm of f
(C) xz is an implicant of f
(D) y is a prime implicant of f


Solution: Every group formed in k map of given function is an implicant of f

Ques 4: Consider a logic circuit shown in figure below. The functions f1,f2 and (in canonical sum of products form in decimal notation) are :

GATE 1997

f1(w,x,y,z) = ∑ 8,9,10
f2(w,x,y,z) = ∑ 7,8,12,13,14,15
f(w,x,y,z)  = ∑ 8,9

The Function f3 is

(A) ∑9,10

(B) ∑9

(C) ∑1,8,9

(D) ∑8,10,18

Ans: (B)

Solution: Output of f1.f2=8

Now output of f=8,9

means input f3 must be 9 or ∑(8,9)

Ques 5: Which of the following functions implements the Karnaugh map shown below?

GATE 1999

(A) A’B+CD

(B) D(C+A)

(C) AD+A’B

(D) (C+D)(C’+D)(A+B)

Ans: (B)


=CD + AD

=D(C + A)

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