SEBA Class 9 Computer Science Chapter 1 Question 6 Solutions | Number System Conversions
SEBA Class 9 Computer Science Chapter 1 Question 6 Solutions | Number System Conversions
Looking for SEBA Class 9 Computer Science Chapter 1 Question 6 Solutions? This page provides complete step-by-step answers for all Number System conversion questions. Learn how to convert between Decimal, Binary, Octal, and Hexadecimal using simple methods that are easy to understand. These solved examples are designed according to the latest SEBA syllabus and are ideal for school exams, unit tests, and annual examinations.
(a) Convert 13510 into Binary Number.
To convert a Decimal number into Binary, keep dividing the number by 2. Write every remainder. Finally, read the remainders from bottom to top.
| Division | Quotient | Remainder |
|---|---|---|
| 135 ÷ 2 | 67 | 1 |
| 67 ÷ 2 | 33 | 1 |
| 33 ÷ 2 | 16 | 1 |
| 16 ÷ 2 | 8 | 0 |
| 8 ÷ 2 | 4 | 0 |
| 4 ÷ 2 | 2 | 0 |
| 2 ÷ 2 | 1 | 0 |
| 1 ÷ 2 | 0 | 1 |
Step 2: Read the remainders from bottom to top.
13510 = 100001112
(b) Convert 11001102 into Decimal Number.
Multiply each binary digit by its corresponding power of 2 and add all the values.
1100110₂
| Digit | Power of 2 | Value |
|---|---|---|
| 1 | 2⁶ | 64 |
| 1 | 2⁵ | 32 |
| 0 | 2⁴ | 0 |
| 0 | 2³ | 0 |
| 1 | 2² | 4 |
| 1 | 2¹ | 2 |
| 0 | 2⁰ | 0 |
64 + 32 + 4 + 2 = 102
11001102 = 10210
(c) Convert 110.1102 into Decimal Number.
Convert the integer part and fractional part separately, then add them together.
Integer Part
1×2² + 1×2¹ + 0×2⁰
= 4 + 2 + 0 = 6
Fraction Part
1×2⁻¹ + 1×2⁻² + 0×2⁻³
= 0.5 + 0.25 + 0
= 0.75
6 + 0.75 = 6.75
110.1102 = 6.7510
(d) Convert 35.37510 into Binary Number.
Convert the integer part by dividing by 2 and convert the decimal part by multiplying by 2.
Integer Part: 35₁₀ = 100011₂
Fraction Part:
| Multiply by 2 | Binary Digit |
|---|---|
| 0.375 × 2 = 0.75 | 0 |
| 0.75 × 2 = 1.50 | 1 |
| 0.50 × 2 = 1.00 | 1 |
35.37510 = 100011.0112
(e) Convert 26510 into Octal Number.
Divide the decimal number by 8 repeatedly and read the remainders from bottom to top.
| Division | Quotient | Remainder |
|---|---|---|
| 265 ÷ 8 | 33 | 1 |
| 33 ÷ 8 | 4 | 1 |
| 4 ÷ 8 | 0 | 4 |
26510 = 4118
(f) Convert 250.37510 into Octal Number.
Convert the whole number and decimal part separately. Divide the whole number by 8 and multiply the decimal part by 8.
Integer Part
250₁₀ = 372₈
Fraction Part
| Multiply by 8 | Octal Digit |
|---|---|
| 0.375 × 8 = 3.000 | 3 |
250.37510 = 372.38
๐ Quick Revision
- Decimal → Binary = Divide by 2
- Binary → Decimal = Powers of 2
- Decimal → Octal = Divide by 8
- Decimal Fraction → Binary = Multiply by 2
- Decimal Fraction → Octal = Multiply by 8
(Part 2A): Carry Out the Following Conversions
Continue learning number system conversions with these solved examples. Follow the easy methods and practice them for your Class IX Computer Science examination.
(g) Convert 3758 into Decimal Number.
To convert an Octal number into Decimal, multiply each digit by the corresponding power of 8 and then add the results.
Step 1: Write the place values.
| Digit | Place Value | Calculation |
|---|---|---|
| 3 | 8² | 3 × 64 = 192 |
| 7 | 8¹ | 7 × 8 = 56 |
| 5 | 8⁰ | 5 × 1 = 5 |
Step 2: Add all the values.
192 + 56 + 5 = 253
3758 = 25310
Octal → Decimal means multiply each digit by powers of 8.
(h) Convert 3758 into Decimal Number.
This question is exactly the same as Question (g), so the solution will also be the same.
3 × 8² = 192
7 × 8¹ = 56
5 × 8⁰ = 5
192 + 56 + 5 = 253
3758 = 25310
Always check the base of the number before starting the conversion.
(i) Convert 25.68 into Decimal Number.
Convert the integer part and fractional part separately. Finally, add both answers.
Step 1: Convert the Integer Part
| Digit | Place Value | Calculation |
|---|---|---|
| 2 | 8¹ | 2 × 8 = 16 |
| 5 | 8⁰ | 5 × 1 = 5 |
Integer Part = 16 + 5 = 21
Step 2: Convert the Fraction Part
| Digit | Place Value | Calculation |
|---|---|---|
| 6 | 8⁻¹ | 6 ÷ 8 = 0.75 |
Fraction Part = 0.75
Step 3: Add Both Parts
21 + 0.75 = 21.75
25.68 = 21.7510
For digits after the decimal point, use negative powers of the base (8⁻¹, 8⁻², ...).
๐ Quick Revision
- Octal → Decimal = Multiply each digit by powers of 8.
- Digits after the decimal point use negative powers like 8⁻¹, 8⁻².
- Always convert the integer part and fractional part separately.
- Add the two answers to get the final decimal number.
(Part 2B): Carry Out the Following Conversions
In this section, you will learn how to convert numbers between the Hexadecimal and Decimal number systems. These questions are frequently asked in Class IX Computer Science examinations.
(j) Convert 12516 into Decimal Number.
To convert a hexadecimal number into decimal, multiply each digit by the corresponding power of 16 and add all the values.
Step 1: Write the place values.
| Digit | Place Value | Calculation |
|---|---|---|
| 1 | 16² | 1 × 256 = 256 |
| 2 | 16¹ | 2 × 16 = 32 |
| 5 | 16⁰ | 5 × 1 = 5 |
Step 2: Add all the values.
256 + 32 + 5 = 293
12516 = 29310
Always remember that in hexadecimal, the base is 16. Therefore, use powers of 16 while converting to decimal.
(k) Convert 43610 into Hexadecimal Number.
To convert a decimal number into hexadecimal, divide the number repeatedly by 16. Read the remainders from bottom to top.
Step 1: Divide by 16.
| Division | Quotient | Remainder |
|---|---|---|
| 436 ÷ 16 | 27 | 4 |
| 27 ÷ 16 | 1 | 11 (B) |
| 1 ÷ 16 | 0 | 1 |
Step 2: Read the remainders from bottom to top.
1 B 4
43610 = 1B416
In hexadecimal,
A = 10
B = 11
C = 12
D = 13
E = 14
F = 15
(l) Convert 213.0312510 into Hexadecimal Number.
Convert the whole number and decimal part separately. Divide the whole number by 16 and multiply the fractional part by 16.
Step 1: Convert the Integer Part
| Division | Quotient | Remainder |
|---|---|---|
| 213 ÷ 16 | 13 | 5 |
| 13 ÷ 16 | 0 | 13 (D) |
Read the remainders from bottom to top.
Integer Part = D5
Step 2: Convert the Fraction Part
| Calculation | Hex Digit |
|---|---|
| 0.03125 × 16 = 0.5 | 0 |
| 0.5 × 16 = 8.0 | 8 |
Fraction Part = .08
Step 3: Combine Both Parts
D5 + .08 = D5.08
213.0312510 = D5.0816
Multiply the decimal fraction repeatedly by 16. The whole number obtained after each multiplication becomes the next hexadecimal digit.
๐ Quick Revision
- Hexadecimal → Decimal = Multiply each digit by powers of 16.
- Decimal → Hexadecimal = Divide repeatedly by 16.
- Read the remainders from bottom to top.
- Hexadecimal digits use A = 10, B = 11, C = 12, D = 13, E = 14, F = 15.
- For decimal fractions, multiply repeatedly by 16.
๐ฏ Exam Tip
Students often confuse hexadecimal digits with decimal numbers. Always remember that A to F represent the values 10 to 15. Practising a few conversions every day will help you solve these questions quickly in the examination.
(Part 3A): Carry Out the Following Conversions
In this section, you will learn how to convert numbers between the Hexadecimal, Decimal, and Binary number systems. Follow the simple steps carefully to score full marks in your examination.
(m) Convert 55.0816 into Decimal Number.
Convert the whole number and decimal part separately using the powers of 16. Then add both answers.
Step 1: Convert the Integer Part
| Digit | Place Value | Calculation |
|---|---|---|
| 5 | 16¹ | 5 × 16 = 80 |
| 5 | 16⁰ | 5 × 1 = 5 |
Integer Part = 80 + 5 = 85
Step 2: Convert the Fraction Part
| Digit | Place Value | Calculation |
|---|---|---|
| 0 | 16⁻¹ | 0 × 1/16 = 0 |
| 8 | 16⁻² | 8 ÷ 256 = 0.03125 |
Fraction Part = 0.03125
Step 3: Add Both Parts
85 + 0.03125 = 85.03125
55.0816 = 85.0312510
Digits after the decimal point use negative powers like 16⁻¹, 16⁻², etc.
(n) Convert 11001101112 into Hexadecimal Number.
Group the binary digits into groups of 4 from right to left. Add leading zeros if needed.
Step 1: Make Groups of Four
1100110111₂
Add two zeros to the left.
0011 0011 0111
Step 2: Convert Each Group
| Binary | Hexadecimal |
|---|---|
| 0011 | 3 |
| 0011 | 3 |
| 0111 | 7 |
Combine all the digits.
11001101112 = 33716
Binary → Hexadecimal always means grouping the digits into 4 bits.
(o) Convert 10011001.101110012 into Hexadecimal Number.
Group the digits into groups of 4 on both sides of the decimal point and convert each group separately.
Step 1: Group the Digits
10011001.10111001
1001 1001 . 1011 1001
Step 2: Convert Each Group
| Binary | Hexadecimal |
|---|---|
| 1001 | 9 |
| 1001 | 9 |
| 1011 | B |
| 1001 | 9 |
Combine both parts.
10011001.101110012 = 99.B916
Binary → Hexadecimal means making groups of 4 bits on both sides of the decimal point.
๐ Quick Revision
- Hexadecimal → Decimal = Multiply by powers of 16.
- Binary → Hexadecimal = Group digits into 4 bits.
- Add leading zeros if the leftmost group has fewer than four bits.
- Convert the integer part and fractional part separately.
- Hexadecimal digits are: 0–9, A, B, C, D, E and F.
๐ฏ Exam Tip
Many students forget to add leading zeros while grouping binary digits into groups of four. Always complete each group before converting it to hexadecimal.
(Part 3B): Carry Out the Following Conversions
This is the final part of the solved conversions. In this section, you will learn how to convert numbers between Hexadecimal, Binary, and Octal number systems using simple and easy steps.
(p) Convert B59E16 into Binary Number.
Replace each hexadecimal digit with its equivalent 4-bit binary number and then join all the groups together.
Step 1: Write the Binary Equivalent
| Hexadecimal Digit | Binary Equivalent |
|---|---|
| B | 1011 |
| 5 | 0101 |
| 9 | 1001 |
| E | 1110 |
Step 2: Join all the Binary Digits
1011 0101 1001 1110
B59E16 = 10110101100111102
Every hexadecimal digit is always equal to 4 binary bits.
(q) Convert 10011001112 into Octal Number.
Group the binary digits into groups of 3 from right to left. Add leading zeros if necessary.
Step 1: Make Groups of Three
1001100111₂
Add two zeros to the left.
001 001 100 111
Step 2: Convert Each Group
| Binary | Octal |
|---|---|
| 001 | 1 |
| 001 | 1 |
| 100 | 4 |
| 111 | 7 |
Join all the octal digits.
10011001112 = 11478
Binary → Octal always means grouping the binary digits into 3 bits.
(r) Convert 60178 into Binary Number.
Replace each octal digit with its corresponding 3-bit binary number and combine all the groups.
Step 1: Write the Binary Equivalent
| Octal Digit | Binary Equivalent |
|---|---|
| 6 | 110 |
| 0 | 000 |
| 1 | 001 |
| 7 | 111 |
Step 2: Join all the Groups
110 000 001 111
60178 = 1100000011112
Every octal digit is always equal to 3 binary bits.
๐ Chapter Revision
- Decimal → Binary = Divide by 2.
- Binary → Decimal = Use powers of 2.
- Decimal → Octal = Divide by 8.
- Octal → Decimal = Use powers of 8.
- Decimal → Hexadecimal = Divide by 16.
- Hexadecimal → Decimal = Use powers of 16.
- Binary → Octal = Group binary digits into 3 bits.
- Binary → Hexadecimal = Group binary digits into 4 bits.
- Octal → Binary = Replace every octal digit with 3 binary bits.
- Hexadecimal → Binary = Replace every hexadecimal digit with 4 binary bits.
๐ฏ Final Exam Tips
- ✔️ Always write the base of every number correctly.
- ✔️ Remember the conversion rules for Binary, Octal and Hexadecimal.
- ✔️ Group Binary digits into 3 bits for Octal and 4 bits for Hexadecimal.
- ✔️ Read the remainders from bottom to top when converting Decimal into Binary, Octal or Hexadecimal.
- ✔️ Practice these conversions regularly to improve your speed and accuracy in the examination.
๐ Keep Practising!
Practice more Number System conversion questions to improve your problem-solving skills. The more you practise, the easier these questions become in your Class IX Computer Science examination.
Frequently Asked Questions (FAQs)
Find answers to the most commonly asked questions about the Number System chapter for Class IX Computer Science.
1. What is a Number System?
A Number System is a method of representing numbers using different digits or symbols. The most common number systems are Decimal (Base 10), Binary (Base 2), Octal (Base 8), and Hexadecimal (Base 16).
2. Why is Binary Number System important?
Computers understand only Binary numbers because electronic circuits have only two states: ON (1) and OFF (0). Therefore, every instruction and data inside a computer is stored in Binary form.
3. What is the base of the Decimal Number System?
The Decimal Number System has a base of 10. It uses ten digits (0–9).
4. What is the base of the Binary Number System?
The Binary Number System has a base of 2. It uses only two digits: 0 and 1.
5. How do you convert Decimal to Binary?
Divide the decimal number repeatedly by 2. Write the remainders and read them from bottom to top.
6. How do you convert Binary to Decimal?
Multiply each binary digit by its corresponding power of 2 and add all the values.
7. How do you convert Decimal to Octal?
Divide the decimal number repeatedly by 8. Read the remainders from bottom to top.
8. How do you convert Binary to Hexadecimal?
Group the binary digits into groups of four starting from the right. Convert each group into its hexadecimal equivalent.
9. Which Number System is used by humans?
Humans generally use the Decimal Number System because it has ten digits (0–9).
10. Which Number System is used by computers?
Computers use the Binary Number System because electronic devices work using two states: ON and OFF.
Conclusion
We hope these Class 9 Computer Science Chapter 1 Number System solved conversions have helped you understand the topic clearly. Learning the step-by-step conversion methods between Decimal, Binary, Octal, and Hexadecimal makes solving examination questions much easier.
Practice each conversion regularly and revise the shortcut methods given above. These questions are important for your Class IX examinations and are frequently asked in school tests and annual exams.
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