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K-Map

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Question 1

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

A
B
C
D
E	None of the above

Digital-Logic-DesignK-MapGATE 1996

Question 1 Explanation:

Correct option is

Question 2

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

A
B	xz is a minterm of f
C	xz is an implicant of f
D	y is a prime implicant of f

Digital-Logic-DesignK-MapGATE 1997

Question 2 Explanation:

In sum of terms,any term is an implicant because it implies the function. So xz is an implicant and hence 'C' is the answer.

Question 3

Consider the Karnaugh map given below, where X represents “don’t care” and blank represents 0.

Assume for all inputs , the respective complements are also available. The above logic is implemented using 2-input NOR gates only. The minimum number of gates required is _________.

A	1
B	2
C	3
D	4

Digital-Logic-DesignK-MapGATE 2017 [Set-1]Video-Explanation

Question 3 Explanation:

Given K-Map represents the function f(a, b, c, d) = a'c = a'(c')' = (a + c')'
As all variables and their complements are available we can implement the function with only one NOR Gate.

Question 4

The function represented by the Karnaugh map given below is:

A	A⋅B
B	AB+BC+CA
C
D	None of the above

Digital-Logic-DesignK-MapGATE 1998

Question 4 Explanation:

Question 5

Which of the following functions implements the Karnaugh map shown below?

A
B
C
D

Digital-Logic-DesignK-MapGATE 1999

Question 5 Explanation:

⇒ CD+AD = D(A+C)

Question 6

Which function does NOT implement the Karnaugh map given below?

A	(w + x)y
B	xy + yw
C
D	None of the above

Digital-Logic-DesignK-MapGATE 2000

Question 6 Explanation:

Given k-map gives xy + xy + wz

⇒ wy + wz + xy

Question 7

Given the following Karnaugh map, which one of the following represents the minimal Sum-Of-Products of the map?

A	xy+y'z
B	wx'y'+xy+xz
C	w'x+y'z+xy
D	xz+y

Digital-Logic-DesignK-MapGATE 2001

Question 7 Explanation:

⇒ y'z + xy

Question 8

Minimum sum of product expression for f(w,x,y,z) shown in Karnaugh-map below is

A	xz+y'z
B	xz'+zx'
C	x'y+zx'
D	None of the above

Digital-Logic-DesignK-MapGATE 2002

Question 8 Explanation:

⇒ xz' + zx'

Question 9

The literal count of a boolean expression is the sum of the number of times each literal appears in the expression. For example, the literal count of (xy + xz') is 4. What are the minimum possible literal counts of the product-of-sum and sum-of-product representations respectively of the function given by the following Karnaugh map ? Here, X denotes "don't care"

A	(11, 9)
B	(9, 13)
C	(9, 10)
D	(11, 11)

Digital-Logic-DesignK-MapGATE 2003

Question 9 Explanation:

For SOP,

⇒ w'y' + z'wx' + xyz'
Total 8 literals are there.
For POS,

⇒ (z' + w')(z' + y')(w' + x')(x + z + w)
Total 9 literals are there.

Question 10

Which are the essential prime implicants of the following Boolean function?

 f(a,b,c) = a^ȼc + ac^ȼ + b^ȼc

A	a^ȼc and ac^ȼ
B	a^ȼc and b^ȼc
C	a^ȼc only
D	ac^ȼ and bc^ȼ

Digital-Logic-DesignK-MapGATE 2004

Question 10 Explanation:

From given function 'f' we can draw,

There are two EPI,
A'C and AC'.

There are 10 questions to complete.

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