### Previous IES Questions on Number Systems, Binary Codes and 1's and 2's Complements

1. Find the value of ‘r’, if √(41)r = (7)10. (1988)

2. Find the number of 1’s in an unsigned binary representation of given number. 163*9 + 162*7 + 16*5 + 3. (1991)

3. Find the number of 1’s in an unsigned binary representation of given number. 3 * 4096 + 15 * 256 + 5 * 16 + 3. (1995)

4. Find the value of ‘r’, if √(224)r = (13)r. (1997)
a. 10
b. 8
c. 5
d. 6

5. Convert the following: (1993)
a. 110.011(2) = X(10)
b. 1118(10) = Y(H)

6. Consider a 3 bit error detection and 1 bit error correction hamming code for 4 bit data. The extra parity bits required would be ________________, and to detect 3 bit error, the minimum distance of the code should be ____________. (1992)

7. In 2’s compliment arithmetic, explain the condition for overflow. (1992)

8. Following 7 bit single error correcting Hamming coded message is received as 1000110. Determine if the message is correct, by assuming that at most 1-bit error could be corrected. If the message contains an error, find the bit which is erroneous and give the correct message. (1994)

9. What is the distance of the following code? If the code contains 000000, 010101, 000111, 011001 and 111111. (1995)
a. 2
b. 3
c. 4
d. 1

10. The octal representation of an integer is 342(8). If this were to be treated as an 8 bit integer in an 8085 based computer, its decimal representation is ________. (1998)
a. 226
b. – 98
c. 76
d. – 30

11. Zero has two representations in___________ (1999)
a. Sign magnitude
b. 1’s complement
c. 2’s complement
d. Both a and b

12. The number 43 in 2’s complement representation is (2000)
a. 01010101
b. 11010101
c. 00101011
d. 10101011

13. 2’s complement representation of (– 539)10 in hexadecimal is (2001)
a. ABE
b. DBC
c. DE5
d. 9E7

14. What is equivalent value for the decimal value 0.25 (2002)
a. 0.1(2)
b. 0.01(2)
c. 0.00111…(2)
d. Can’t be represented precisely

15. 2’s complement representation of decimal value (– 15) is (2002)
a. 1111
b. 11111
c. 111111
d. 10001

16. Assume all numbers are in 2’s complement form, which of the following numbers is divisible by 11111011? (2003)
a. 11100111
b. 11100100
c. 11010111
d. 11011011

17. If 73(x) = 54(y) then the possible values of x and y are (2004 & 2011)
a. 8, 16
b. 10,12
c. 9,13
d. 8,11

18. Let A = 11111010 and B = 00001010 be two 8-bit 2’s complement numbers. Their product in 2’complement is (2004)
a. 11000100
b. 10011100
c. 10100101
d. 11010101

19. An 8085 microprocessor executes the following instructions: Two numbers are represented in signed 2’s complement form as P = 11101101 and Q = 11100110. If Q is subtracted from P, the value obtained in signed 2’s complement form is (2012)
a. 100000111
b. 00000111
c. 11111001
d. 011111001

20. If (11X1Y)8 = (12C9)16 then the values of X and Y are (2012)
a. 3, 1
b. 5, 7
c. 7, 5
d. 1, 5

21. Binary data is being represented in size of byte and in 2’s complement form. The number of 0’s present in representation of (– 127)10 is (2012)
a. 8
b. 7
c. 6
d. 5

22. The decimal equivalent of binary number 10110.11 is (2013)
a. 16.75
b. 20.75
c. 16.50
d. 22.75

23. Hexadecimal conversion of decimal number 227 will be (2013)
a. A3
b. E3
c. CC
d. C3

24. A seven bit Hamming code is received as 1111101. What is the correct code? (2013)
a. 1101111
b. 1011111
c. 1111111
d. 1111011

25. The number of 1’s present in the binary representation of 15*256 + 5*16 + 3 are (2014)
a. 8
b. 9
c. 10
d. 11

26. Given (135)X + (144)X = (323)X. what is the value of x? (2005 & 2014)
a. 5
b. 3
c. 12
d. 6

27. Which one of the following is correct answer when 11011(2) is subtracted from 11101(2) by using 1’s complement method? (2015)
a. 01001
b. 10001
c. 00011
d. 00010

28. An Excess-3 code arithmetic operation is used to perform (2015)
b. Binary subtraction
d. BCD subtraction

29. Convert the decimal 41.6875 into octal (2015)
a. 51.54
b. 51.13
c. 54.13
d. 51.51

30. The decimal equivalent of binary 110.001 is (2015)
a. 6.25
b. 6.125
c. 62.5
d. 0.612

31. Given (125)r = (203)5. The value of r will be (2015)
a. 16
b. 10
c. 8
d. 6

32. The 9’s complement of (25.639)10 is (2015)
a. 74.360
b. 0.6732
c. 6.732
d. 7.436

33. If (2.3)4 + (1.2)4 = (Y)4, then what is the value of Y? (2005)
a. 10.1
b. 10.01
c. 10.2
d. 1.02

34. The number of 1’s in 8-bit representation of – 127 in 2’s complement form is ‘m’ and that in 1’s complement form is ‘n’. What is the value of m:n? (2005)
a. 2:1
b. 1:2
c. 3:1
d. 1:3

35. Assertion (A): There is no overflow after an addition, if one number is positive and the other is negative.
Reason (R): Adding a positive number to a negative number always produces a result, which is smaller than the larger of the two. (2005)
a. Both A and R are individually true and R is the correct explanation of A
b. Both A and R are individually true and R is not the correct explanation of A
c. A is true but R is false
d. A is false but R is true

36. A Gray code is a/an___________ (2005)
a. Binary weight code
b. Arithmetic code
c. Code which exhibits a single bit change between two consecutive codes
d. Alphanumeric code

37. Which of the following subtraction operations do not result in F16?
1. (BA)16 – (AB)16
2. (BC)16 – (CB)16
3. (CB)16 – (BC)16
Select the correct answer using the codes given below: (2006)
a. Only 1 and 2
b. Only 1 and 3
c. Only 2 and 3
d. All, 1 , 2 and 3

38. What is the Gray code word for the binary number 101011? (2006)
a. 101011
b. 110101
c. 011111
d. 111110

39. What is the addition of (– 64)10 and (80)16? (2007)
a. (– 16)10
b. (16)16
c. (1100000)2
d. (01000000)2

40. (24)8 is expressed in Gray code. Which one of the following is correct? (2008)
a. 11000
b. 10100
c. 11110
d. 11111

41. Two 2’s complement numbers having sign bits ‘x’ and ‘y’ are added and the sign bit of the result is ‘z’. which Boolean function indicates overflow condition? (2008)
a. xyz
b. x’y’z’
c. x’y’z + xyz’
d. xy + yz + zx

42. Consider the following statements: (2009)
1. Taking 2’s complement is equivalent to sign change
2. In the 2’s complement representation, the MSB is zero for a positive number
3. In a 4 bit binary representation of a binary number A, A + 1’s complement of A = 24.
Which of the above statements are correct?
a. 1 and 2 only
b. 1 and 3 only
c. 2 and 3 only
d. 1, 2 and 3

43. The hexadecimal representation of (657)8 is (2010)
a. 1AFH
b. D78H
c. D71H
d. 32FH

44. Find radix ‘r’, if √(41)r = 5(10).

45. Find radix, if 302/20 = 12.1

46. In a positional weight system, x and y are two successive digits and xy = 25(10) and yx = 31(10). Determine radix, x and y.

### Network Synthesis & Driving Point Impedance - Topicwise GATE Questions on Network Theory (from 2003)

2005
1. The first and Last critical frequency of an RC driving point impedance function must respectively be
a) a zero and a pole
b) a zero and a zero
c) a pole and a pole
d) a pole and a zero

2006
2. The first and the last critical frequencies (singularities) of a driving point impedance function of a passive network having two kinds of elements, are a pole and a zero respectively. The above property will be satisfied by
a) RL network only
b) RC network only
c) LC network only
d) RC as well as RL networks

3. A negative resistance Rneg is connected to a passive network N having driving point impedance Z1(s) as shown below. For Z2(s) to be positive real,

2008
4. The driving point impedance of the following network is given as shown. The component values are

### Steady State Analysis of AC and DC circuits - Topicwise GATE Questions on Network Theory (from 2003)

2005
1. For the circuit in figure, the instantaneous current i1(t) is

2007
2. In the AC network shown in the figure, the phasor voltage VAB(in volts) is:

2008
Common Data Questions: 3 & 4
The following series RLC circuit with zero initial conditions is excited by a unit impulse function δ(t).

3. For t > 0, the output voltage Vc(t) is

4. For t > 0, the voltage across the resistor is

Solution (3 & 4) : https://www.youtube.com/watch?v=nn6PggFjKgA

2009
5. The time domain behaviour of an RL circuit is represented as shown below. For an initial current of i(0) = Vo/R, the steady state value of the current is given by

2010
6. The current I in the circuit shown is

a) - j1 A
b) j1 A
c) 0 A
d) 20 A

2011
7. In the circuit shown below, the Norton equivalent current in amperes with respect to the terminals P and Q is

a) 6.4 - j 4.8
b) 6.56 - j 7.87
c) 10 + j 0
d) 16 + j 0

8. The circuit shown below is driven by a sinusoidal input Vi = Vpcos(t/RC). The steady state output Vo is

9. In the circuit shown below, the current I is equal to

2012
10. In the circuit shown below, the current through the inductor is

2014
11. In the circuit shown in the figure, the value of node voltage V2 (in volts) is

a) 22 + j 2
b) 2 + j 22
c) 22 – j 2
d) 2 – j 22

12. The steady state output of the circuit shown in the figure is given by y(t) = A(ω) sin(ωt + φ(ω)).

If the amplitude |A(ω)| = 0.25, then the frequency ω is

13. In the circuit shown in the figure,

the value of Vo(t) (in volts) for t → ∞ is ___________

2015
14. In the circuit shown, assume that diodes D1 and D2 are ideal. In the steady state condition, the average voltage Vab (in volts) across 0.5 µF capacitor is ____________

### Resonance (Series and Parallel) - Topicwise GATE Questions on Network Theory (from 2003)

2003
1. A series RLC circuit has a resonance frequency of 1 kHz and a quality factor Q = 100. If each R, L and C is doubled from its original value, the new Q-factor of the circuit is
a) 25
b) 50
c) 100
d) 200

2004
2. Consider the following statements S1 and S2
S1: at the resonant frequency, the impedance of a series RLC circuit is zero.
S2: In a parallel G-L-C circuit, increasing the conductance G results in increase in its Q-factor.
Which one of the following is correct?
a) S1 is FALSE and S2 is TRUE
b) Both S1 and S2 are TRUE
c) S1 is TRUE and S2 is FALSE
d) Both S1 and S2 are FALSE

2005
3. The condition on R, L and C such that the step response y(t) in figure has no oscillations, is

4. In a series RLC circuit, R = 2 kΩ, L = 1 H, and C = 1/400 µF. The resonant frequency is
a) 2 x 104 Hz
b) (1/π) x 104 Hz
c) 104 Hz
d) 2π x 104 Hz

2007
5. Two series resonant filters are as shown in the figure. Let the 3-dB bandwidth of filter 1 is B1 and that of Filter 2 is B2. The value of B1/B2 is

a) 4
b) 1
c) 1/2
d) 1/4

2010
6. For parallel RLC circuit, which one of the following statements is NOT correct?
a) The bandwidth of the circuit decreases if R is increased
b) The bandwidth of the circuit remains same if L is increased
c) At resonance, input impedance is a real quantity
d) At resonance, the magnitude of input impedance attains its minimum value.

2013
7. Two magnetically uncoupled inductive coils have Q factors q1 and q2 at the chosen operating frequency. Their respective resistances are R1 and R2. When connected in series, their effective Q factor at the same operating frequency is
a) q1 + q2
b) (1/q1) + (1/q2)
c) (q1R1 + q2R2) / (R1 + R2)
d) (q1R2 + q2R1) / (R1 + R2)

2014
8. In the circuit shown in the figure, the value of capacitor C (in mF) needed to have critically damped response i(t) is ____________________

9. A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such that the current leads the supply voltage. The magnitude of current is half the value at resonance. If the values of L, C and R are 1H, 1F and 1Ω respectively, then the operating angular frequency (in rad/sec) is ____________________

10. In the circuit shown in the figure, the angular frequency ω (in rad/sec), at which the Norton equivalent impedance as seen from terminals b – b' is purely resistive, is _____________

2015
11. In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in volts) across the capacitor is ____________________

12. The voltage (Vc) across the capacitor (in volts) in the network shown is ______________

13. An LC tank circuit consists of an ideal capacitor C connected in parallel with a coil of inductance L having an internal resistance R. The resonant frequency of the tank circuit is