Free Printable GATE-DLD-Kmap

1.

The SOP (sum of products) form of a Boolean function is Σ(0,1,3,7,11), where inputs are A,B,C,D

(A is MSB, and D is LSB). The equivalent minimized expression of the function is[GATE-EE-2014]

a)

$\left(\overline{B}\ +C\right)\left(\overline{A}\ +C\right)$

$\left(\overline{A}\ +\overline{B}\right)\left(\overline{C}\ +D\right)$

b)

$\left(\overline{B}\ +C\right)\left(\overline{A}\ +C\right)$

$\left(\overline{A}\ +\overline{C}\right)\left(\overline{C}\ +D\right)$

c)

$\left(\overline{B}\ +C\right)\left(\overline{A}\ +C\right)$

$\left(\overline{A}\ +\overline{C}\right)\left(\overline{C}\ +\overline{D}\right)$

d)

$\left(\overline{B}\ +C\right)\left(A\ +\overline{B}\right)$

$\left(\overline{A}\ +\overline{B}\right)\left(\overline{C}+D\right)$

2.

$f\left(A,B,C,D\right)=\Pi M\left(0,1,3,4,5,7,9,11,12,13,14,15\right)$ is a maxterm representation of a Boolean function f(A,B,C,D) where A is the MSB and D is LSB. The equivalent minimized representation of the function is [GATE-EE-2015]

a)

$\left(A+\overline{C}\ +D\right)\left(\overline{A}\ +B+D\right)$

b)

$A\overline{C}\ D+\overline{A}\ BD$

c)

$\overline{A}\ C\ \overline{D}\ +A\overline{B}\ C\overline{D}\ +A\overline{B}\ \overline{C}\ \overline{D}$

d)

$\left(B+\overline{C}\ +D\right)$

$\left(A+\overline{B}\ +\overline{C}+D\right)$

$\left(\overline{A}\ +B+C+D\right)$

3.

D igital input signals 𝐴, 𝐵, 𝐶 with 𝐴 as the MSB and 𝐶 as the LSB are used to realize the

Boolean function 𝐹 = 𝑚0 + 𝑚2 + 𝑚3 + 𝑚5 + 𝑚7, where⁡𝑚𝑖 ⁡denotes⁡the⁡𝑖𝑡ℎ⁡minterm. In

addition, 𝐹 has a don’t care for 𝑚1. The simplified expression for 𝐹 is given by [GATE-EE-2018]

a)

$\overline{A}\ \overline{C}\ +\overline{B}\ C\ +AC$

b)

$\overline{A}\ +C$

c)

$\overline{C}\ +A$

d)

$\overline{A}\ C+BC+A\overline{C}$

4.

Given f(A,B,C,D)= $\Sigma m\left(0,1,2,6,8,9,10,11\right)+\Sigma d\left(3,7,14,15\right)\$ is a Boolean function, where m represents min-terms and d represents don't cares. The minimal sum of products expression for f is [GATE-IN-2020]

a)

$f=A\overline{B}\ +BC$

b)

$f=\overline{B}+C$

c)

$f=A+\overline{D}$

d)

$f=\overline{A}\ B+\overline{C}\ D$

5.

T he product of sum expression of a Boolean function 𝐹(𝐴, 𝐵, 𝐶) of three variables is given by

𝐹(𝐴, 𝐵, 𝐶) = $\left(A+B+\overline{C}\right)\left(A+\overline{B}\ +\overline{C}\right)\left(\overline{A}\ +B+C\right)\left(\overline{A}\ +\overline{B}\ +\overline{C}\right)$

The canonical sum of product expression of 𝐹(𝐴, 𝐵, 𝐶) is given by [GATE-IN-2018]

a)

$\overline{A}\ \overline{B}\ C+\overline{A}\ BC+A\overline{B}\ \overline{C}\ +ABC$

b)

$\overline{A}\ \ \overline{B}\ \overline{C}+\overline{A}B\overline{C}+A\overline{B}C+AB\overline{C}$

c)

$AB\overline{C}\ +A\overline{B}\ \overline{C}\ +\overline{A}\ BC+\overline{A}\ \overline{B}\ \overline{C}$

d)

$\overline{A}\ \overline{B}\ \overline{C}+\overline{A}BC+AB\overline{C}\ +ABC$

6.

The simplified form of the Boolean function F (𝑊,𝑋,𝑌,𝑍) = Σ (4, 5, 10, 11, 12, 13, 14, 15) with the minimum number of terms and smallest number of literals in each term is_________.[GATE-IN-2023]

a)

$WX+\overline{W}\ X\overline{\ Y}\ +W\overline{X}Y$

b)

$WX+WY+X\overline{Y}$

c)

$X\overline{Y}+WY$

d)

$\overline{X}\ Y+\overline{W}\ \overline{Y}$

7.

For the Boolean function F(A,B,C,D)=∑m(0,2,5,7,8,10,12,13,14,15) the essential prime implicants are _________[GATE-ECE-2024]

a)

$BD,\overline{B}\ \overline{D}$

b)

BD,AB

c)

$AB.\ \overline{B}\ \overline{D}$

d)

$\overline{B}\ \overline{D}\ ,BD,AB$

8.

Which one of the following gives the simplified sum of products expression for the Boolean function F=m0+m2+m3+m5, where F=m0+m2+m3+m5, are minterms corresponding to the inputs A, B and C with A as the MSB and C as the LSB?

a)

$\overline{A}\ B+\overline{A}\ \overline{B}\ \overline{C}+A\overline{B}C$

b)

$\overline{A}\ \overline{C}+\overline{A}\ B+A\overline{B}C$

c)

$\overline{A}\ \overline{C}+A\overline{B}+A\overline{B}\ C$

d)

$\overline{A}\ BC+\overline{A}\ \overline{C}\ +A\overline{B}\ C$

9.

Following is the k-map of a Boolean function of five variable P, Q, R, S and X. The minimum for the function is[GATE ECE 2016]

a)

$\overline{P}\ \overline{Q}\ S\overline{X}\ +P\overline{Q}S\overline{X}\ +Q\overline{R}\ \overline{S}\ X+QR\overline{S}\ X$

b)

$\overline{Q}\ S\overline{X}\ +Q\overline{S}\ X$

c)

$\overline{Q}\ SX+Q\overline{S}\ \overline{X}$

d)

$\overline{Q}S+Q\overline{S}$

10.

Consider a Boolean expression given by F(X,Y,Z)=Σ(3,5,6,7).

Which of the following statements is/are CORRECT? [GATE CSE 2024]

a)

F(X,Y,Z)=Π(0,1,2,4)

b)

F(X,Y,Z)=XY+YZ+XZ

c)

F(X,Y,Z) is independent of input Y

d)

F(X,Y,Z) is independent of input X

11.

Consider the Boolean function z(a,b,c).Which one of the following minterm lists represents the circuit given above?[GATE CSE 2020]

a)

z = ∑(0,1,3,7)

b)

z = ∑(1,4,5,6,7)

c)

z = ∑(2,4,5,6,7)

d)

z = ∑(2,3,5)

12.

The output expression for the Karnaugh map shown below is[GATE EE 2017]

a)

$B\overline{D}\ +BCD$

b)

$B\overline{D}\ +AB$

c)

$\overline{B}\ D+ABC$

d)

$B\overline{D}+ABC$

13.

Which of the following logic circuits is a realization of the function F whose karnaugh map is shown in figure[GATE EE 2014]

a)

b)

c)

d)

14.

A minimized form of the function F is [GATE EE 2010]

a)

$F=\overline{X}\ \overline{Y}\ +YZ$

b)

$F=\overline{X}\ \overline{Y}\ +\overline{Y}\ \overline{Z}$

c)

$F=\overline{X}\ \overline{Y}\ +Y\overline{Z}$

d)

$F=\overline{X}\ \overline{Y}\ +\overline{Y}Z$

15.

Consider the following interm expression of F: F(P,Q,R,S)=∑0,2,5,7,8,10,13,15
The minterms 2,7,8 and 13 are 'do not care' terms. The minimal sum-of-products form for F is _______[GATE CSE 2014]

a)

$Q\overline{S}\ +\overline{Q}\ S$

b)

$\overline{Q}\ \overline{S}\ +QS$

c)

$\overline{Q}\ \overline{R}\ \overline{S}\ +\overline{Q}\ R\overline{S}\ +Q\overline{R}\ S+QRS$

d)

$\overline{P}\ \overline{Q}\ \overline{S}\ +\overline{P}\ QS+PQS+P\overline{Q}\ \overline{S}$

16.

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? [GATE CSE 2008]

a)

$\overline{b}\ .\overline{d\ }\ +\overline{a}\ .\overline{d\ }$

b)

$\overline{a}\ \overline{b}\ +\overline{b}\ \overline{d\ }+\overline{a}\ \overline{b}\ \overline{d\ }$

c)

$\overline{b}\ \overline{d\ }+\overline{a}\ \overline{b}\ \overline{d\ }$

d)

$\overline{a}\ \overline{b}\ +\overline{b}\ \overline{d\ }+\overline{a}\ \overline{a}\ \overline{d\ }$

17.

Minimum SOP for f(w,x,y,z) shown in karnaugh − map below is [GATE CSE 2002]

a)

x z+y'z

b)

x z'+z x'

c)

x'y+z x'

d)

None

18.

Given the following Karnaugh map, which one of the following represents the minimal Sum-Of-Products of the map?[GATE CSE 2001]

a)

xy+y'z

b)

wx'y'+xy+xz

c)

w'x+y'z+xy

d)

xz+y

19.

Consider the minterm list form of a Boolean function 𝐹 given below. F(P,Q,R,S)= ∑m(0,2,5,7,9,11) +d(3,8,10,12,14) Here, m denotes a minterm and d denotes a don’t care term. The number of essential prime implicants of the function F is (a) .[GATE CSE 2018]

20.

What is the minimal form of the Karnaugh map shown below? Assume that X denotes a don’t care term.[GATE CSE 2012]

a)

$\overline{b}\ \overline{d\ }$

b)

$\overline{b}\ \overline{d\ }+\overline{b}\ \overline{c}$

c)

$\overline{b}\ \overline{d\ }\ +a\overline{b}\ \overline{c}\ d$

d)

$\overline{b}\ \overline{d\ }+\overline{b}\ \overline{c}\ +\overline{c}\ \overline{d\ }$

GATE-DLD-Kmap

Total questions: 20

Worksheet time: 22mins

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