Number Systems — TN Class 11 Computer Science Exercise Solutions
Complete exercise solutions for the Tamil Nadu Board Class 11 Computer Science chapter Number Systems. Covers binary, octal, decimal, and hexadecimal conversions with step-by-step worked examples.
How to Use This Page
1. Attempt each exercise on your own first — work through conversions on paper before checking answers. 2. Verify every step — conversion mistakes often come from wrong positional values or grouping errors. 3. Understand the method — don't just memorise answers; know why each step works. 4. Practice similar problems — change the numbers and redo conversions until the method is automatic. 5. Use the Key Concepts table for a quick review before solving.
Key Concepts (Quick Recap)
| Number System | Base | Digits Used | Place Value |
|---|---|---|---|
| Decimal | 10 | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 | Powers of 10 |
| Binary | 2 | 0, 1 | Powers of 2 |
| Octal | 8 | 0, 1, 2, 3, 4, 5, 6, 7 | Powers of 8 |
| Hexadecimal | 16 | 0–9, A(10), B(11), C(12), D(13), E(14), F(15) | Powers of 16 |
Hexadecimal Digit Mapping:
| Decimal | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Hex | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |
Conversion Summary:
| From → To | Method |
|---|---|
| Binary → Decimal | Multiply each bit by its positional power of 2 and add |
| Decimal → Binary | Repeated division by 2; read remainders bottom to top |
| Octal → Decimal | Multiply each digit by its positional power of 8 and add |
| Decimal → Octal | Repeated division by 8; read remainders bottom to top |
| Hexadecimal → Decimal | Multiply each digit by its positional power of 16 and add |
| Decimal → Hexadecimal | Repeated division by 16; read remainders bottom to top |
| Binary → Octal | Group bits in 3s from right; convert each group |
| Octal → Binary | Convert each octal digit to 3-bit binary |
| Binary → Hexadecimal | Group bits in 4s from right; convert each group |
| Hexadecimal → Binary | Convert each hex digit to 4-bit binary |
I. Choose the Best Answer (MCQs)
Q1. The base of the binary number system is: (a) 2 (b) 8 (c) 10 (d) 16
Binary uses only two digits (0 and 1). The base (radix) of a number system equals the number of distinct digits it uses.
Q2. The binary equivalent of decimal 10 is: (a) 1010 (b) 1100 (c) 1001 (d) 1110
10 ÷ 2 = 5 R0, 5 ÷ 2 = 2 R1, 2 ÷ 2 = 1 R0, 1 ÷ 2 = 0 R1. Reading remainders bottom to top: 1010.
Q3. In the hexadecimal system, the digit A represents the decimal value: (a) 0 (b) 10 (c) 11 (d) 16
Hexadecimal digits go 0–9, then A=10, B=11, C=12, D=13, E=14, F=15.
Q4. The octal equivalent of binary 110101 is: (a) 65 (b) 56 (c) 74 (d) 47
Group in 3s from right: 110 101 → 6 5 → 65 in octal.
Q5. Which number system is used internally by computers? (a) Decimal (b) Binary (c) Octal (d) Hexadecimal
Computers use binary (base 2) internally because digital circuits have two states: ON (1) and OFF (0), corresponding to high and low voltage levels.
Q6. The decimal value of hexadecimal 1F is: (a) 31 (b) 21 (c) 15 (d) 35
1F = 1 × 16¹ + F × 16⁰ = 16 + 15 = 31.
Q7. How many digits are there in the octal number system? (a) 2 (b) 8 (c) 10 (d) 16
The octal system (base 8) uses eight digits: 0, 1, 2, 3, 4, 5, 6, 7.
II. Fill in the Blanks
1. The base of the decimal number system is 10. 2. In the binary number system, each digit is called a bit. 3. The hexadecimal digit F equals the decimal value 15. 4. The octal number 10 equals the decimal number 8. 5. To convert binary to octal, group the binary digits in sets of 3 from the right. 6. To convert binary to hexadecimal, group the binary digits in sets of 4 from the right. 7. The binary equivalent of octal 7 is 111. 8. The decimal number 255 in hexadecimal is FF. 9. The binary number 1000 represents decimal 8. 10. Each octal digit can be represented by 3 binary digits. 11. Each hexadecimal digit can be represented by 4 binary digits. 12. The hexadecimal digit B equals decimal 11. 13. The binary equivalent of decimal 2 is 10. 14. The decimal value of binary 1111 is 15.
III. True or False (with corrections for false statements)
IV. Match the Following
| Column A | Column B |
|---|---|
| 1. Binary | (d) Base 2 |
| 2. Octal | (e) Base 8 |
| 3. Decimal | (a) Base 10 |
| 4. Hexadecimal | (f) Base 16 |
| 5. Bit | (b) Binary digit |
| 6. Nibble | (c) 4 bits |
| Column A | Column B |
|---|---|
| 1. Hex A | (b) Decimal 10 |
| 2. Hex C | (d) Decimal 12 |
| 3. Hex F | (f) Decimal 15 |
| 4. Octal 10 | (a) Decimal 8 |
| 5. Binary 1000 | (c) Decimal 8 |
| 6. Binary 1111 | (e) Decimal 15 |
V. Answer Briefly (2-Mark Questions)
VI. Answer in Detail (5-Mark Questions)
Common Mistakes to Avoid
1. Wrong positional values in conversion — When converting binary 1011 to decimal, start powers from the right (2⁰, 2¹, 2², 2³), not from the left.
2. Reading remainders in the wrong order — When converting decimal to another base, read remainders from bottom to top (last remainder is the most significant digit).
| 3. Incorrect grouping for binary-to-octal — Group from the right. For 110101, groups are 110 | 101, not 111 | 0101. Pad with leading zeros on the left if needed. |
|---|
4. Forgetting to pad binary groups — When converting octal 3 to binary, write 011 (3 bits), not just 11. When converting hex 3 to binary, write 0011 (4 bits), not just 11.
5. Mixing up hex digit values — A=10, B=11, C=12, D=13, E=14, F=15. A is NOT 1 and F is NOT 16.
6. Arithmetic errors in positional calculations — Double-check multiplication and addition. Common error: 1×2⁴ = 16, not 8.
7. Not verifying answers — Always convert your answer back to the original base to verify. If decimal 10 → binary 1010, check: 1×8 + 0×4 + 1×2 + 0×1 = 10 ✓
Exam Checklist
Before your exam, make sure you can:
- [ ] Name the four number systems with their bases and digits
- [ ] Convert any binary number to decimal (multiply by positional powers)
- [ ] Convert any decimal number to binary (repeated division by 2)
- [ ] Convert between binary and octal (group/expand by 3 bits)
- [ ] Convert between binary and hexadecimal (group/expand by 4 bits)
- [ ] Convert between decimal and octal/hexadecimal (repeated division)
- [ ] Recall hex digit values: A=10 through F=15
- [ ] Identify when to group from the right (binary → octal/hex)
- [ ] Verify conversions by converting back to the original base
- [ ] Explain why computers use binary internally