Chapter 2: Number System
Section A: Multiple Choice Questions (30 Marks)
1. What is the base or radix of the Binary number system?
2. The Decimal number system uses how many total digits (0 through 9)?
3. Which number system has a base of 8 and consists of digits from 0 to 7?
4. In the Hexadecimal number system, what letter represents the decimal value 10?
5. What is the base of the Hexadecimal number system?
6. What is the single binary digit (0 or 1) called in computer memory terminology?
7. A combination of 8 bits grouped together is called a:
8. A group of 4 bits is specifically known as a:
9. In binary addition, what is the result of 1 + 1?
10. What is the binary equivalent of the decimal number 5?
11. What is the binary equivalent of the decimal number 10?
12. Convert binary number (111)₂ into its equivalent Decimal number:
13. In binary subtraction, what is 1 - 1 equal to?
14. In binary subtraction, 0 - 1 requires borrowing 1 from the next higher position, making the value:
15. What is the product of binary multiplication 1 × 0?
16. In Hexadecimal, what decimal value does the letter F represent?
17. To convert a Decimal number to Binary, we repeatedly divide the decimal number by:
18. When converting decimal to binary, the remainders are recorded from:
19. In a positional number system, the rightmost digit is called the:
20. In a positional number system, the leftmost digit with the highest positional weight is the:
21. Calculate the binary addition: (101)₂ + (011)₂:
22. What is the value of 2⁰ in positional place values?
23. Computer systems internal circuits are constructed using digital electronic switches that represent states:
24. Calculate binary subtraction: (110)₂ - (010)₂:
25. In binary arithmetic, what is 1 + 1 + 1 equal to?
26. Which symbol is NOT a valid digit in the Octal number system?
27. Calculate binary multiplication: (101)₂ × (10)₂:
28. Calculate binary division: (110)₂ ÷ (10)₂:
29. How is the Hexadecimal digit C represented in decimal?
30. Convert decimal number 12 into Binary:
Section B: Assertion & Reason Questions (30 Marks)
Directions: Choose the correct option for each question:
- A: Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
- B: Both Assertion (A) and Reason (R) are true, but Reason (R) is NOT the correct explanation of Assertion (A).
- C: Assertion (A) is true, but Reason (R) is false.
- D: Assertion (A) is false, but Reason (R) is true.
31. Assertion (A): Computers process and store data internally using the Binary number system.
Reason (R): Computer circuits are made of digital electronic switches that easily represent two stable states: ON (1) and OFF (0).
32. Assertion (A): The number (89)₈ is a valid number in the Octal number system.
Reason (R): Octal number system uses only 8 digits, from 0 to 7, so digits 8 and 9 are invalid.
33. Assertion (A): In Hexadecimal, the letter 'E' represents the decimal value 14.
Reason (R): Hexadecimal uses digits 0-9 followed by letters A through F to represent values 10 to 15.
34. Assertion (A): In binary addition, 1 + 1 generates a sum of 0 and a carry of 1.
Reason (R): The decimal sum 2 is represented as (10)₂ in binary code.
35. Assertion (A): A group of 8 bits is referred to as a Nibble.
Reason (R): A Nibble consists of 4 bits, whereas a Byte consists of 8 bits.
36. Assertion (A): Decimal to binary conversion requires repeated division of the decimal number by 2.
Reason (R): The remainders collected from bottom to top form the target binary string.
37. Assertion (A): In binary subtraction, 0 - 1 = 1 with a borrow of 1 from the next higher position.
Reason (R): Borrowing 1 from the adjacent position converts the 0 into binary (10)₂, which equals decimal 2, and 2 - 1 = 1.
38. Assertion (A): Hexadecimal numbers are widely used by programmers to shorten long binary representations.
Reason (R): One single Hexadecimal digit can exactly represent a group of 4 binary bits.
39. Assertion (A): The base of any number system specifies the maximum number of unique symbols/digits used in that system.
Reason (R): Decimal number system has base 10 because it uses 10 distinct digits (0 to 9).
40. Assertion (A): Binary multiplication rules are completely different from elementary decimal multiplication.
Reason (R): Multiplying 1 × 0 or 0 × 1 in binary yields 0, exactly like decimal multiplication.
41. Assertion (A): The binary number (1010)₂ is equal to decimal 10.
Reason (R): (1 × 2³) + (0 × 2²) + (1 × 2¹) + (0 × 2⁰) = 8 + 0 + 2 + 0 = 10.
42. Assertion (A): Non-positional number systems rely on positional weights assigned to each digit location.
Reason (R): Non-positional number systems like Roman numerals use symbols with static values regardless of position.
43. Assertion (A): In the binary number 1101₂, the rightmost digit '1' represents the place value 2⁰ = 1.
Reason (R): In positional number systems, the rightmost digit is the Least Significant Digit (LSD) with weight base⁰.
44. Assertion (A): Binary division follows long division principles similar to decimal division.
Reason (R): Division by zero is valid and gives a quotient of 1 in binary arithmetic.
45. Assertion (A): The Octal system uses digits from 0 to 8.
Reason (R): Octal is a base-8 number system, so its digits range from 0 to 7.
46. Assertion (A): Converting a binary number to decimal involves multiplying each bit by increasing powers of 2.
Reason (R): Powers of 2 start from 2⁰ at the rightmost bit and increase by 1 for each position to the left.
47. Assertion (A): In Hexadecimal notation, 'B' corresponds to decimal 11.
Reason (R): The sequence goes A=10, B=11, C=12, D=13, E=14, F=15.
48. Assertion (A): 1 + 1 + 1 in binary yields a sum digit of 1 and a carry digit of 1.
Reason (R): Decimal 3 is converted to binary as 11₂ (1 group of 2 plus 1 unit).
49. Assertion (A): Binary arithmetic can only be performed on positive numbers.
Reason (R): Specialized techniques like 2's complement are used by computers to handle negative binary numbers.
50. Assertion (A): Any number raised to the power 0 equals 1.
Reason (R): Thus, 2⁰ = 1, 8⁰ = 1, 10⁰ = 1, and 16⁰ = 1 in positional expansions.
51. Assertion (A): The decimal equivalent of binary 100₂ is 4.
Reason (R): (1 × 2²) + (0 × 2¹) + (0 × 2⁰) = 4 + 0 + 0 = 4.
52. Assertion (A): Human beings naturally use the Decimal number system in daily counting.
Reason (R): The decimal system likely originated because humans have 10 fingers for counting.
53. Assertion (A): Binary subtraction 1 - 0 equals 0.
Reason (R): Subtracting 0 from any binary digit leaves the original digit unchanged.
54. Assertion (A): Hexadecimal digit '10' is written as 'A'.
Reason (R): Single-character symbols are required for values 10-15 to avoid confusion with two decimal digits.
55. Assertion (A): The most significant digit (MSD) carries the least weight in a number.
Reason (R): MSD is the leftmost digit in a positional number having the maximum positional weight.
56. Assertion (A): Binary multiplication 1 × 1 equals 1.
Reason (R): Multiplying two active ON state bits results in an active ON state bit.
57. Assertion (A): Octal conversion is often used as a convenient shorthand for binary numbers.
Reason (R): Each octal digit directly maps to a 3-bit binary sequence (since 2³ = 8).
58. Assertion (A): In binary division 101₂ ÷ 1₂, the answer is 101₂.
Reason (R): Dividing any binary number by 1 leaves the original binary number unchanged.
59. Assertion (A): The place values in binary system move right to left as 1, 2, 4, 8, 16, 32...
Reason (R): These positional weights represent powers of base 2 (i.e., 2⁰, 2¹, 2², 2³, 2⁴...).
60. Assertion (A): Binary addition is fundamental to all arithmetic operations in microprocessors.
Reason (R): Microprocessors perform subtraction, multiplication, and division internally through addition circuits.
Section C: Image & Visual Feature Based Questions (10 Marks)
61. Identify the division table structure visual:
2 | 25 | Remainder
2 | 12 | 1 (LSD)
2 | 6 | 0
2 | 3 | 0
2 | 1 | 1
| 0 | 1 (MSD)
Reading remainders from bottom to top, what is the binary equivalent of Decimal 25?
62. Observe the positional expansion chart visual:
Binary: 1 0 1 1
Weights: 2³ 2² 2¹ 2⁰
Values: 8 0 2 1
What is the total sum in decimal value?
63. Identify the binary addition vertical alignment visual:
1 1 (Carries)
1 0 1 1₂
+ 0 1 1 0₂
-----------
1 0 0 0 1₂
What is the decimal equivalent of the final result (10001₂)?
64. Scenario Visual: Rashmi is writing a program in memory representation using groups of 4 bits: 1010. What hexadecimal character represents this 4-bit nibble?
65. Identify the Hexadecimal mapping visual:
Hex Digit: 9 | A | B | C | D | E | F
Decimal: 9 | 10 | 11 | [?] | 13 | 14 | 15
What decimal value replaces the question mark [?] for Hex digit C?
66. Observe the binary subtraction with borrowing visual:
0 2 (Borrowed value)
1 0₂
- 0 1₂
-----
0 1₂
What is the decimal equivalent of binary 10₂ minus 01₂?
67. Scenario Visual: Mohit creates a table comparing memory storage sizes:
1 Bit = Single 0 or 1
4 Bits = 1 [ ? ]
8 Bits = 1 Byte
What term correctly fills the question mark [ ? ] for 4 bits?
68. Identify the number system base classification visual:
Binary ➔ Base 2
Octal ➔ Base 8
Decimal ➔ Base 10
Hexadecimal ➔ Base [ ? ]
What base number fills the bracket [ ? ]?
69. Look at the binary multiplication layout visual:
1 1₂ (Decimal 3)
× 1 0₂ (Decimal 2)
-------
0 0
+ 1 1 0
-------
1 1 0₂ (Decimal [?])
What decimal value replaces [?] for the binary result 110₂?
70. Identify the digit significance labels in number (4582)₁₀:
4 ➔ Most Significant Digit (MSD)
2 ➔ Least Significant Digit (LSD)
What positional weight does the MSD digit '4' hold in this decimal number?