Digital Logic Test 2

Question 1
2 / -0.33

Consider a quadratic equation x2 – 13x + 36 = 0 with coefficients in a base b. The solutions of this equation in the same base b are x = 5 and x = 6. Then b = _______.

A
7

B
8

C
9

D
10

Question 2
2 / -0.33

A function (A, B, C) defined by three boolean variables A, B, and C when expressed as the sum of products is given by:
F = A̅.B̅.C̅ + A̅.B.C̅ + A.B̅.C̅
where, A̅, B̅, and C̅ are the complements of the respective variables. The product of sums (POS) form of the function F is

A
F = (A + B + C) . (A + B̅ + C) . (A̅ + B + C)

B
F = (A̅ + B̅ + C̅) . (A̅ + B + C̅) + (A + B̅ + C̅)

C
F = (A + B + C̅) . (A + B̅ + C̅) . (A̅ + B + C̅) . (A̅ + B̅ + C) . (A̅ + B̅ + C̅)

D
F = (A̅ + B̅ + C) . (A̅ + B + C) . (A + B̅ + C) . (A + B + C̅) . (A + B + C)

Question 3
2 / -0.33

What are the first eight bits of mantissa part and the decimal value stored in exponent if (-28.375)10 is represented in single-precision IEEE 754 format?

A
Mantissa = 11000110

B
Exponent = 132

C
Mantissa = 11100011

D
Exponent = 131

Question 4
2 / -0.33

In the following truth table, V = 1 if and only if the input is valid.
Inputs
Outputs
D₀
D₁
D₂
D₃
X₀
X₁
V
0
0
0
0
x
x
0
1
0
0
0
0
0
1
x
1
0
0
0
1
1
x
x
1
0
1
0
1
x
x
x
1
1
1
1

What function does the truth table represent?

A
Priority encoder

B
Decoder

C
Multiplexer

D
Demultiplexer

Question 5
2 / -0.33

The clock frequency of 12 MHz is applied to a cascaded counter of modulus-4 counter, modulus-5 counter and modulus-6 counter.

A
The overall modulus of the cascaded counter is 60

B
The lowest output frequency of the cascaded counter is 100 kHz

C
The overall modulus of the cascaded counter is 120

D
The lowest output frequency of the cascaded counter is 200 kHz

Question 6
2 / -0.33

The simplified Sum of Product form of the following Boolean expression:
\((P + \bar Q + \bar R )(P + Q+R)(P+Q+\bar R )\) is

A
\(\bar P Q+R\)

B
\(P+Q\bar R \)

C
\(P\bar Q +R\)

D
\(PQ+ R\)

Question 7
2 / -0.33

Consider the unsigned 8-bit point binary number representation below:
X₇X₆X₅X₄ .X₃X₂X₁X₀
where the position of the binary point is between X₄ and X₃. X₇ is the MSB. Which of the decimal numbers cannot be represented exactly in the above representation:
(a) 14.1875
(b) 16.125
(c) 3.03125
(d) 1.6875

A
Only a and c

B
Only b and c

C
Only b and d

D
All (a), (b), (c) and (d)

Question 8
2 / -0.33

Consider the function F = A + B̅C, where F is a three-variable Boolean function in which A is MSB and C is LSB. Which of the following is/are false among the given options?

A
F = ∑ (1, 4, 5, 6, 7)

B
F = ∑ (1, 3, 5, 6, 7)

C
F = ∏ (0, 2, 4)

D
F = ∏ (0, 2, 3)

Question 9
2 / -0.33

Consider the 64-bit register which stops floating point number in IEEE Double precision format
What is the value of the number if 64 bits are given below?
1
10000000111
010111000…

A
-348--348

B
-3484--3481

C
-3487--3486

D
-3489--3482

Question 10
2 / -0.33

P, Q, and R are the decimal integers corresponding to the 4-bit binary number 1100 considered in signed magnitude, 1’s complement, and 2’s complement representations, respectively. The 6-bit 2’s complement representation of (P + Q + R) is

A
110101

B
110010

C
111101

D
111001

Question 11
2 / -0.33

How many functions does f1.f2 and f1 + f2 represents respectively if the given function is
\({\rm{f}}1{\left( {{\rm{a}},{\rm{b}},{\rm{c}}} \right)_{}} = \mathop \sum \nolimits_M \;\left( {0,{\rm{\;}}1,{\rm{\;}}4} \right) + {\rm{\;}}\mathop \sum \limits_\emptyset \left( {3,{\rm{\;}}5,{\rm{\;}}7} \right)\)
\({\rm{f}}2\left( {{\rm{a}},{\rm{b}},{\rm{c}}} \right) = \mathop \sum \nolimits_M \;\left( {2,3} \right) + {\rm{\;}}\mathop \sum \limits_\emptyset \left( {1,{\rm{\;}}6,{\rm{\;}}7} \right)\)
where ∑_m represents sum of min-terms and ∑_ϕ represents and don’t care

A
2, 4

B
8, 8

C
4, 8

D
4, 4

Question 12
2 / -0.33

D input of a clocked D-flip-flop receives and input A ⊕ Q_n where A is an external logic input and Q_n is the output of the n^th D-FF before the clock appears. The circuit works as

A
EXOR gate

B
T-FF

C
D-FF

D
JK-FF

Submit Test

Inputs				Outputs
D₀	D₁	D₂	D₃	X₀	X₁	V
0	0	0	0	x	x	0
1	0	0	0	0	0	1
x	1	0	0	0	1	1
x	x	1	0	1	0	1
x	x	x	1	1	1	1

Digital Logic T...

Question 1

7

8

9

10

Question 2

F = (A + B + C) . (A + B̅ + C) . (A̅ + B + C)

F = (A̅ + B̅ + C̅) . (A̅ + B + C̅) + (A + B̅ + C̅)

F = (A + B + C̅) . (A + B̅ + C̅) . (A̅ + B + C̅) . (A̅ + B̅ + C) . (A̅ + B̅ + C̅)

F = (A̅ + B̅ + C) . (A̅ + B + C) . (A + B̅ + C) . (A + B + C̅) . (A + B + C)

Question 3

Mantissa = 11000110

Exponent = 132

Mantissa = ​11100011

Exponent = 131

Question 4

Priority encoder

Decoder

Multiplexer

Demultiplexer

Question 5

The overall modulus of the cascaded counter is 60

The lowest output frequency of the cascaded counter is 100 kHz

The overall modulus of the cascaded counter is 120

The lowest output frequency of the cascaded counter is 200 kHz

Question 6

\(\bar P Q+R\)

\(P+Q\bar R \)

\(P\bar Q +R\)

\(PQ+ R\)

Question 7

Only a and c

Only b and c

Only b and d

All (a), (b), (c) and (d)

Question 8

F = ∑ (1, 4, 5, 6, 7)

F = ∑ (1, 3, 5, 6, 7)

F = ∏ (0, 2, 4)

F = ∏ (0, 2, 3)

Question 9

-348--348

-3484--3481

-3487--3486

-3489--3482

Question 10

110101

110010

111101

111001

Question 11

2, 4

8, 8

4, 8

4, 4

Question 12

EXOR gate

T-FF

D-FF

JK-FF

User

Question Analysis

Mantissa = 11100011