# Logic functions and Minimization

 Question 1
Which one of the following expressions does NOT represent exclusive NOR of x and y?
 A xy+x'y' B x⊕y' C x'⊕y D x'⊕y'
GATE CS 2013    Digital Logic & Number representation    Logic functions and Minimization
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Question 1 Explanation:
By Definition of XNOR, So Option-A is correct. Also by Definition of XOR, Option-B is So Option-B is also correct. Option-C is Option-C is also correct. Option-D x'⊕y' = x''y' + x'y'' = xy' + x'y = x⊕y ≠ x⊙y Therefore option (D) is false. This explanation is provided by Chirag Manwani.
 Question 2
What is the minimal form of the Karnaugh map shown below? Assume that X denotes a don’t care term. A b'd' B b'd' + b'c' C b'd' + a'b'c'd' D b'd' + b'c' + c'd'
Digital Logic & Number representation    Logic functions and Minimization
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Question 2 Explanation:
There are two prime implicants in the following K-Map- Prime Implicant higlighted in Green = Prime Implicant higlighted in Orange = So the Boolean expression is- Therefore option (B) is correct. This explanation is provided by Chirag Manwani.
 Question 3
Which one of the following circuits is NOT equivalent to a 2-input XNOR (exclusive NOR) gate? A A B B C C D D
GATE CS 2011    Digital Logic & Number representation    Logic functions and Minimization
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Question 3 Explanation:
All options except D produce XOR as described below : Question 4
The simplified SOP (Sum Of Product) form of the boolean expression (P + Q' + R') . (P + Q' + R) . (P + Q + R') is
 A (P'.Q + R') B (P + Q'.R') C (P'.Q + R) D (P.Q + R)
GATE CS 2011    Digital Logic & Number representation    Logic functions and Minimization
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Question 4 Explanation:
See following : (P+Q'+R').(P+Q'+R).(P+Q+R') =  From the K-map, POS form is : P + Q'.R'
 Question 5
The minterm expansion of f(P, Q, R) = PQ + QR' + PR' is
 A m2 + m4 + m6 + m7 B m0 + m1 + m3 + m5 C m0 + m1 + m6 + m7 D m2 + m3 + m4 + m5
GATE CS 2010    Digital Logic & Number representation    Logic functions and Minimization
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 Question 6
What is the minimum number of gates required to implement the Boolean function (AB+C)if we have to use only 2-input NOR gates?
 A 2 B 3 C 4 D 5
GATE-CS-2009    Digital Logic & Number representation    Logic functions and Minimization
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Question 6 Explanation:
AB+C = (A+C)(B+C) = ((A+C)' + (B+C)')' So, '3' 2-input NOR gates are required.
 Question 7
In the Karnaugh map shown below, X denotes a don't care term. What is the minimal form of the function represented by the Karnaugh map? A) B) C) D) A A B B C C D D
Digital Logic & Number representation    GATE CS 2008    Logic functions and Minimization
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 Question 8
Given f1, f3 and f in canonical sum of products form (in decimal) for the circuit  A) m(4, 6)

B) m(4, 8)

C) m(6, 8)

D) m(4, 6, 8)
 A A B B C C D D
Digital Logic & Number representation    GATE CS 2008    Logic functions and Minimization
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Question 8 Explanation:
From logic diagram  we have f=f1.f2+f3 f=m(4,5,6,7,8).f2+m(1,6,15)----(1) from eq(1) we need to find such f2 so that we can get  f=m(1,6,8,15) eq(1)  says we can get m(1,6,15) from f3 ,so only  8 left now from option (a,b,d) we get (4,6), (4,8) ,(4,6,8) respectively for m(4,5,6,7,8)f2 which is not required as m4 is undesired. But option (C) m(4,5,6,7,8)(6,8)+(1,6,15)
• m(6,8)+m(1,6,15)
• m(1,6,8,15)an
Option (C) is correct.
 Question 9
If P, Q, R are Boolean variables, then (P + Q')(PQ' + PR)(P'R' + Q') simplifies
 A PQ' B PR' C PQ' + R D PR'' + Q
Digital Logic & Number representation    GATE CS 2008    Logic functions and Minimization
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Question 9 Explanation:
(P + Q')(PQ' + PR)(P'R' + Q') = (P + Q)(PQ + PRQ') = (P + Q)(PQ') = PQ' So, option (A) is correct.
 Question 10
Consider the following Boolean function of four variables: f(w,x,y,z) = ∑(1,3,4,6,9,11,12,14) The function is:
 A independent of one variables. B independent of two variables. C independent of three variables. D dependent on all the variables.
Digital Logic & Number representation    GATE-CS-2007    Logic functions and Minimization
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Question 10 Explanation: On solving K-MAP we get ZX’+XZ’ so  it is independent of w,y Ans (B) part.
There are 101 questions to complete.
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