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)
Ans:(C)
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
=z’+x
=(x*y)’ + x
=(x’+y)’ + x
= x.y’ + x
=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
Answer:(C)
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 f (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)
Solution:
=CD + AD
=D(C + A)