Number Systems and Boolean Algebra MCQs Quiz (BCA 1st Sem)

1. What is the base of the Decimal Number System?

A) 2
B) 8
C) 10
D) 16

Correct Answer: C) 10

2. Which number system uses only the digits 0 and 1?

A) Decimal
B) Octal
C) Binary
D) Hexadecimal

Correct Answer: C) Binary

3. How many digits are used in the Binary Number System?

A) 2
B) 8
C) 10
D) 16

Correct Answer: A) 2

4. What is the base value of the Octal Number System?

A) 2
B) 8
C) 10
D) 16

Correct Answer: B) 8

5. In the Decimal Number System, what is the position value of the digit in position 2?

A) 10²
B) 10¹
C) 10³
D) 10⁴

Correct Answer: A) 10²

6. What is the base value of the Hexadecimal Number System?

A) 2
B) 8
C) 10
D) 16

Correct Answer: D) 16

7. Which notation represents a number in base 16?

A) (101)₂
B) (345)₈
C) (23)₁₀
D) (1A3)₁₆

Correct Answer: D) (1A3)₁₆

8. What is the quantity of the digit in position 0 in the Binary Number System?

A) 1
B) 2
C) 4
D) 8

Correct Answer: A) 1

9. In the Binary Number System, what is the position value of the digit in position 3?

A) 2⁰
B) 2¹
C) 2²
D) 2³

Correct Answer: D) 2³

10. How is a number expressed in base 8 indicated in notation?

A) (number)₁₀
B) (number)₂
C) (number)₈
D) (number)₁₆

Correct Answer: C) (number)₈

11. In the Decimal Number System, what is the position value of the digit in position -2?

A) 10^-2
B) 10^-1
C) 10⁰
D) 10¹

Correct Answer: A) 10^-2

12. What is the position value of the digit in position 1 in the Binary Number System?

A) 2⁰
B) 2¹
C) 2²
D) 2³

Correct Answer: B) 2¹

13. How many digits are used in the Hexadecimal Number System?

A) 10
B) 12
C) 16
D) 2

Correct Answer: C) 16

14. In which number system is the number (1101) most commonly used in computing?

A) Decimal
B) Binary
C) Octal
D) Hexadecimal

Correct Answer: B) Binary

15. In the Decimal Number System, what is the position value of the digit in position 3 of the number 5965?

A) 100
B) 10¹
C) 10²
D) 10³

Correct Answer: D) 10³

16. What is the quantity of the digit in position -3 in the Binary Number System?

A) 1/2
B) 1/4
C) 1/8
D) 1/16

Correct Answer: C) 1/8

17. What is the base of the octal number system?

A) 2
B) 8
C) 10
D) 16

Correct Answer: B) 8

18. Which digits are used in the octal number system?

A) 0 to 9
B) 0 to 7
C) 0 to F
D) 1 to 8

Correct Answer: B) 0 to 7

19. What is the base of the hexadecimal number system?

A) 8
B) 10
C) 12
D) 16

Correct Answer: D) 16

20. Which of the following is NOT a valid octal number?

A) 273
B) 103
C) 8F7
D) 2375

Correct Answer: C) 8F7

21. Which of the following digits is used to represent the decimal value 15 in hexadecimal?

A) E
B) F
C) D
D) 9

Correct Answer: B) F

22. In hexadecimal, what decimal value does the letter 'B' represent?

A) 10
B) 11
C) 12
D) 13

Correct Answer: B) 11

23. Which of the following is a valid hexadecimal number?

A) 1A2
B) 29G
C) 56H
D) 12Z

Correct Answer: A) 1A2

24. What is the octal representation of the decimal number 8?

A) 8
B) 10
C) 18
D) 7

Correct Answer: B) 10

25. Which of the following digits is NOT used in the hexadecimal number system?

A) 5
B) 7
C) G
D) D

Correct Answer: C) G

26. How many unique digits are there in the hexadecimal number system?

A) 8
B) 10
C) 12
D) 16

Correct Answer: D) 16

27. What is the position value of the second digit from the right in an octal number?

A) 8⁰
B) 8¹
C) 8²
D) 8³

Correct Answer: B) 8¹

28. In the number 2A3 (hexadecimal), what is the position value of 'A'?

A) 16⁰
B) 16¹
C) 16²
D) 16³

Correct Answer: B) 16¹

29. Which hexadecimal digit represents the highest value?

A) 9
B) A
C) F
D) E

Correct Answer: C) F

30. If the octal number is 345, what is the position value of the digit '4'?

A) 8⁰
B) 8¹
C) 8²
D) 8³

Correct Answer: B) 8¹

31. In the hexadecimal number 3FA, what is the decimal equivalent of 'F'?

A) 13
B) 14
C) 15
D) 16

Correct Answer: C) 15

32. What is the smallest digit used in both octal and hexadecimal number systems?

A) 0
B) 1
C) 2
D) 3

Correct Answer: A) 0

33. What is the maximum digit in the octal number system?

A) 6
B) 7
C) 8
D) 9

Correct Answer: B) 7

34. Which of the following numbers is valid in both octal and hexadecimal systems?

A) 1A2
B) 137
C) 8B7
D) 29G

Correct Answer: B) 137

35. Which of the following is the position value of the third digit from the right in a hexadecimal number?

A) 16⁰
B) 16¹
C) 16²
D) 16³

Correct Answer: C) 16²

36. What is the decimal equivalent of the octal number 17?

A) 14
B) 15
C) 16
D) 17

Correct Answer: B) 15

37. What is the procedure used to convert a decimal integer to binary?

A) Divide by 2
B) Multiply by 2
C) Divide by 8
D) Multiply by 8

Correct Answer: A) Divide by 2

38. How do you convert a decimal fraction to binary?

A) Divide by 2
B) Multiply by 2
C) Divide by 8
D) Multiply by 8

Correct Answer: B) Multiply by 2

39. What is the first step in converting a decimal integer fraction to any other base?

A) Convert the decimal fraction portion
B) Convert the decimal integer portion
C) Combine both portions
D) Multiply by the base

Correct Answer: B) Convert the decimal integer portion

40. To convert a decimal fraction to octal, which operation is performed?

A) Divide by 8
B) Multiply by 8
C) Divide by 16
D) Multiply by 16

Correct Answer: B) Multiply by 8

41. What is the result of converting 0.2345 from Base 10 to Base 2?

A) 0.001111
B) 0.100010
C) 0.010111
D) 0.111000

Correct Answer: A) 0.001111

42. How do you convert a binary number to octal?

A) Group the binary digits into groups of four bits
B) Group the binary digits into groups of three bits
C) Convert each group of four bits to decimal
D) Divide the binary number by 8

Correct Answer: B) Group the binary digits into groups of three bits

43. Which base uses groups of four bits when converting from binary?

A) Octal
B) Decimal
C) Hexadecimal
D) Binary

Correct Answer: C) Hexadecimal

44. What is the first step to convert 34.4674 from Base 10 to Base 2?

A) Convert the integer portion to binary
B) Convert the fraction portion to binary
C) Convert the integer portion to hexadecimal
D) Convert the fraction portion to hexadecimal

Correct Answer: A) Convert the integer portion to binary

45. In which position does the digit with the value 0.011001 in binary convert to?

A) Base 8
B) Base 16
C) Base 10
D) Base 2

Correct Answer: C) Base 10

46. What is the decimal equivalent of the binary number 1011.1001?

A) 11.5625
B) 10.6875
C) 12.75
D) 9.875

Correct Answer: A) 11.5625

47. Which of the following is NOT a step in converting binary to hexadecimal?

A) Group the binary digits into sets of four
B) Convert each group of four bits to a hexadecimal digit
C) Convert each group of three bits to a hexadecimal digit
D) Combine the hexadecimal digits

Correct Answer: C) Convert each group of three bits to a hexadecimal digit

48. When converting from octal to decimal, which value is used for the position of the digit?

A) Position increases to the left of the decimal point
B) Position increases to the right of the decimal point
C) Position decreases to the left of the decimal point
D) Position decreases to the right of the decimal point

Correct Answer: A) Position increases to the left of the decimal point

49. To convert a hexadecimal number to decimal, which operation is performed on each digit?

A) Multiply by the base
B) Divide by the base
C) Find the sum of Face Value * (from Base) position
D) Group digits into sets of four

Correct Answer: C) Find the sum of Face Value * (from Base) position

50. How is the binary number 1110101100110 converted to octal?

A) Group the binary digits into sets of three bits
B) Group the binary digits into sets of four bits
C) Convert each group of four bits to octal digits
D) Convert each bit individually

Correct Answer: A) Group the binary digits into sets of three bits

51. What is the decimal equivalent of the octal number 24.36?

A) 20.4375
B) 22.4375
C) 20.75
D) 18.75

Correct Answer: A) 20.4375

52. What is the 1’s complement of the binary number 10101100?

A) 10101101
B) 01010011
C) 01010010
D) 11100011

Correct Answer: B) 01010011

53. In one's complement, what happens to each bit of the binary number?

A) Each 0 is converted to 1, and each 1 is converted to 0
B) Each 0 is multiplied by 1, and each 1 is divided by 2
C) Each bit is left unchanged
D) Each bit is inverted and then multiplied by 2

Correct Answer: A) Each 0 is converted to 1, and each 1 is converted to 0

54. Which of the following represents the 1’s complement of 1101.101?

A) 1010.010
B) 0010.010
C) 0010.010
D) 1110.111

Correct Answer: B) 0010.010

55. Which of the following is NOT an application of 1’s complement?

A) Representing signed binary numbers
B) Binary arithmetic operations like addition
C) Floating-point arithmetic operations
D) Decimal to binary conversion

Correct Answer: D) Decimal to binary conversion

56. What is the 1’s complement representation of the binary number 1010 in 4 bits?

A) 0101
B) 1111
C) 1010
D) 0000

Correct Answer: A) 0101

57. What is the maximum positive integer that can be stored in a 5-bit register using one's complement?

A) 2⁵ - 1
B) 2⁴ - 1
C) 2⁴
D) 2⁵

Correct Answer: B) 2⁴ - 1

58. In one’s complement form, how is -6 represented using 8 bits?

A) 1111 1001
B) 0000 0110
C) 1111 1010
D) 0000 1101

Correct Answer: A) 1111 1001

59. Which of the following is a property of the 1's complement representation?

A) It has two representations for zero: positive zero and negative zero
B) It has a unique representation for zero
C) It uses only unsigned binary numbers
D) It can represent only negative numbers

Correct Answer: A) It has two representations for zero: positive zero and negative zero

60. What is the range of numbers that can be represented using 1’s complement in a 4-bit register?

A) -8 to 7
B) -7 to 7
C) -8 to 8
D) -7 to 8

Correct Answer: B) -7 to 7

61. What is the binary representation of -10 in one's complement using 8 bits?

A) 1111 0101
B) 1111 0100
C) 1111 0110
D) 0000 1010

Correct Answer: A) 1111 0101

62. What is one of the major flaws of using the signed bit method for representing signed integers?

A) Limited number of negative values
B) Two representations of zero
C) Cannot store positive values
D) Sign extension works perfectly

Correct Answer: B) Two representations of zero

63. In the 1’s complement method, how do you represent a negative number?

A) By flipping each bit of the positive number
B) By adding 1 to the positive number
C) By keeping the first bit as the sign bit
D) By adding 2 to the positive number

Correct Answer: A) By flipping each bit of the positive number

64. Which of the following is not a problem with the signed bit method?

A) Two representations of zero
B) Negative numbers work with signed extensions
C) Binary addition doesn’t work
D) Limited storage capacity for values

Correct Answer: B) Negative numbers work with signed extensions

65. In the 2’s complement method, how do you get the binary representation of a negative number?

A) Flip each bit of the positive number
B) Flip each bit of the positive number and add 1
C) Add 2 to the positive number
D) Keep the sign bit and flip the other bits

Correct Answer: B) Flip each bit of the positive number and add 1

66. What is a significant advantage of the 2’s complement method over other methods?

A) Multiple representations of zero
B) Only one representation of zero
C) Sign extension does not work
D) Requires additional hardware

Correct Answer: B) Only one representation of zero

67. In 2’s complement, how can you detect memory overflow?

A) When carry into the signed bit is equal to carry out
B) By checking for multiple representations of zero
C) By checking the first bit for the sign
D) When all bits are set to 1

Correct Answer: A) When carry into the signed bit is equal to carry out

68. What is the primary issue with 1’s complement representation?

A) Negative numbers do not support sign extension
B) Two representations of zero
C) Cannot represent positive numbers correctly
D) Binary subtraction is not possible

Correct Answer: B) Two representations of zero

69. In the signed bit method, what is the role of the leftmost bit?

A) Stores the value of the number
B) Indicates the sign of the number
C) Determines if the number is odd or even
D) Used for overflow detection

Correct Answer: B) Indicates the sign of the number

70. What is a drawback of binary addition using the signed bit method?

A) The sign bit must be handled separately
B) It produces overflow errors
C) It cannot add negative numbers
D) It requires extra bits

Correct Answer: A) The sign bit must be handled separately

71. In 2’s complement, why is the first bit referred to as the signed bit?

A) It indicates the type of number
B) All positive numbers start with 0, and all negative numbers start with 1
C) It determines the number of bits to be used
D) It shows the magnitude of the number

Correct Answer: B) All positive numbers start with 0, and all negative numbers start with 1

72. What is the primary focus of Boolean algebra?

A) Algebra involving decimal numbers and arithmetic operations
B) Algebra involving binary variables and logic operations
C) Algebra involving hexadecimal numbers and conversions
D) Algebra involving algebraic expressions and equations

Correct Answer: B) Algebra involving binary variables and logic operations

73. In Boolean algebra, what is the complement of a variable A denoted as?

A) A'
B) A
C) A''
D) A bar

Correct Answer: D) A bar

74. Which Boolean operation is equivalent to Boolean addition?

A) OR operation
B) AND operation
C) NOT operation
D) XOR operation

Correct Answer: A) OR operation

75. Which Boolean operation is equivalent to Boolean multiplication?

A) OR operation
B) AND operation
C) NOT operation
D) XOR operation

Correct Answer: B) AND operation

76. What does a product term in Boolean algebra require to be equal to 1?

A) All literals must be 1
B) At least one literal must be 1
C) All literals must be 0
D) At least one literal must be 0

Correct Answer: A) All literals must be 1

77. How is a sum term in Boolean algebra determined to be equal to 1?

A) All literals must be 1
B) At least one literal must be 1
C) All literals must be 0
D) At least one literal must be 0

Correct Answer: B) At least one literal must be 1

78. Which law of Boolean algebra is applied in the following expression: A + (B + C) = (A + B) + C?

A) Distributive Law
B) Associative Addition Law
C) Commutative Addition Law
D) Associative Multiplication Law

Correct Answer: B) Associative Addition Law

79. What is the primary function of an inverter gate in Boolean algebra?

A) To perform an AND operation
B) To perform an OR operation
C) To produce the complement of a variable
D) To combine multiple literals

Correct Answer: C) To produce the complement of a variable

80. In the Boolean function F = x + y'z, what does the term y'z represent?

A) An OR operation
B) A NOT operation
C) An AND operation
D) A sum term

Correct Answer: C) An AND operation

81. How many combinations are listed in a truth table for n binary variables?

A) 2^n
B) n^2
C) 2^n - 1
D) n^2 - 1

Correct Answer: A) 2^n

82. Which Boolean algebra rule is illustrated by the expression: A + A = A?

A) Identity Law
B) Idempotent Law
C) Complement Law
D) Distribution Law

Correct Answer: B) Idempotent Law

83. What is the primary use of logic gates in computers?

A) For data conversion between number systems
B) For performing binary arithmetic operations
C) For manipulating binary data in circuits
D) For encoding and decoding information

Correct Answer: C) For manipulating binary data in circuits

84. What is the primary advantage of using Two’s Complement over One’s Complement in binary arithmetic?

A) It simplifies the representation of signed integers
B) It provides easier arithmetic operations and overflow checks
C) It allows for a larger range of positive numbers
D) It is easier to convert between number systems

Correct Answer: B) It provides easier arithmetic operations and overflow checks

85. What does the term "Boolean addition" refer to?

A) The process of combining binary numbers
B) The OR operation in Boolean algebra
C) The AND operation in Boolean algebra
D) The process of finding the complement of a variable

Correct Answer: B) The OR operation in Boolean algebra

86. Which number system uses digits 0-9 and letters A-F?

A) Decimal
B) Binary
C) Octal
D) Hexadecimal

Correct Answer: D) Hexadecimal

✨ BCA JUL24 Batch ✨

Join Our WhatsApp Group

Interactive MCQs Quiz

1. What is the base of the Decimal Number System?

2. Which number system uses only the digits 0 and 1?

3. How many digits are used in the Binary Number System?

4. What is the base value of the Octal Number System?

5. In the Decimal Number System, what is the position value of the digit in position 2?

6. What is the base value of the Hexadecimal Number System?

7. Which notation represents a number in base 16?

8. What is the quantity of the digit in position 0 in the Binary Number System?

9. In the Binary Number System, what is the position value of the digit in position 3?

10. How is a number expressed in base 8 indicated in notation?

11. In the Decimal Number System, what is the position value of the digit in position -2?

12. What is the position value of the digit in position 1 in the Binary Number System?

13. How many digits are used in the Hexadecimal Number System?

14. In which number system is the number (1101) most commonly used in computing?

15. In the Decimal Number System, what is the position value of the digit in position 3 of the number 5965?

16. What is the quantity of the digit in position -3 in the Binary Number System?

17. What is the base of the octal number system?

18. Which digits are used in the octal number system?

19. What is the base of the hexadecimal number system?

20. Which of the following is NOT a valid octal number?

21. Which of the following digits is used to represent the decimal value 15 in hexadecimal?

22. In hexadecimal, what decimal value does the letter 'B' represent?

23. Which of the following is a valid hexadecimal number?

24. What is the octal representation of the decimal number 8?

25. Which of the following digits is NOT used in the hexadecimal number system?

26. How many unique digits are there in the hexadecimal number system?

27. What is the position value of the second digit from the right in an octal number?

28. In the number 2A3 (hexadecimal), what is the position value of 'A'?

29. Which hexadecimal digit represents the highest value?

30. If the octal number is 345, what is the position value of the digit '4'?

31. In the hexadecimal number 3FA, what is the decimal equivalent of 'F'?

32. What is the smallest digit used in both octal and hexadecimal number systems?

33. What is the maximum digit in the octal number system?

34. Which of the following numbers is valid in both octal and hexadecimal systems?

35. Which of the following is the position value of the third digit from the right in a hexadecimal number?

36. What is the decimal equivalent of the octal number 17?

37. What is the procedure used to convert a decimal integer to binary?

38. How do you convert a decimal fraction to binary?

39. What is the first step in converting a decimal integer fraction to any other base?

40. To convert a decimal fraction to octal, which operation is performed?

41. What is the result of converting 0.2345 from Base 10 to Base 2?

42. How do you convert a binary number to octal?

43. Which base uses groups of four bits when converting from binary?

44. What is the first step to convert 34.4674 from Base 10 to Base 2?

45. In which position does the digit with the value 0.011001 in binary convert to?

46. What is the decimal equivalent of the binary number 1011.1001?

47. Which of the following is NOT a step in converting binary to hexadecimal?

48. When converting from octal to decimal, which value is used for the position of the digit?

49. To convert a hexadecimal number to decimal, which operation is performed on each digit?

50. How is the binary number 1110101100110 converted to octal?

51. What is the decimal equivalent of the octal number 24.36?

52. What is the 1’s complement of the binary number 10101100?

53. In one's complement, what happens to each bit of the binary number?

54. Which of the following represents the 1’s complement of 1101.101?

55. Which of the following is NOT an application of 1’s complement?

56. What is the 1’s complement representation of the binary number 1010 in 4 bits?

57. What is the maximum positive integer that can be stored in a 5-bit register using one's complement?

58. In one’s complement form, how is -6 represented using 8 bits?

59. Which of the following is a property of the 1's complement representation?

60. What is the range of numbers that can be represented using 1’s complement in a 4-bit register?

61. What is the binary representation of -10 in one's complement using 8 bits?

62. What is one of the major flaws of using the signed bit method for representing signed integers?

63. In the 1’s complement method, how do you represent a negative number?

64. Which of the following is not a problem with the signed bit method?

65. In the 2’s complement method, how do you get the binary representation of a negative number?

66. What is a significant advantage of the 2’s complement method over other methods?

67. In 2’s complement, how can you detect memory overflow?

68. What is the primary issue with 1’s complement representation?

69. In the signed bit method, what is the role of the leftmost bit?

70. What is a drawback of binary addition using the signed bit method?

71. In 2’s complement, why is the first bit referred to as the signed bit?

72. What is the primary focus of Boolean algebra?

73. In Boolean algebra, what is the complement of a variable A denoted as?

74. Which Boolean operation is equivalent to Boolean addition?

75. Which Boolean operation is equivalent to Boolean multiplication?

76. What does a product term in Boolean algebra require to be equal to 1?

77. How is a sum term in Boolean algebra determined to be equal to 1?