Decimal Numbers to Binary Numbers

Introduction

Modern computation is based on numbers. For the most part, computers utilize the binary (base-2) system, but people use the decimal (base-10) system. Programmers, tech aficionados, and students alike must be able to convert decimal values to binary. This article will teach us the exact steps involved in converting decimals to binary, along with typical examples and practical uses, all presented in an easy-to-understand, student-friendly way.

 

Table Of Content

• What is Number System Conversion ?
• Core Concepts of Decimal to Binary Conversion
• How to Convert Decimal Numbers to Binary (Step-by-Step)
• Decimal to Binary Conversion Chart (1–20)
• Applications of Decimal to Binary Conversion
• Common Mistakes & Tips
• Decimal to Binary Practice Problems
• Decimal to Binary Converter Examples
• Real-life Usage
• Conclusion
• Related Links
• FAQs

What is Number System Conversion?

The process of converting numbers from one base (such as decimal) to another (such as binary) is known as number system conversion. In computer science, where the binary number system is used to process information, this is particularly crucial.

 

Core Concepts of Decimal to Binary Conversion

Decimal Number System (Base-10)

• Digits used are 0 to 9

• Each digit’s place value is a power of 10
  Example: 453 = (4 × 10²) + (5 × 10¹) + (3 × 10⁰)
  
  

Binary Number System (Base-2)

• Uses only two digits: 0 and 1

• Each digit’s place value is a power of 2
  Example: 1011 = (1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰) = 8 + 0 + 2 + 1 = 11
  
  

How to Convert Decimal Numbers to Binary (Step-by-Step)

Here’s how to convert any whole number from decimal to binary:

Step-by-Step Method (Division by 2)

1. Divide the decimal number by 2

2. Record the remainder (0 or 1)

3. Divide the quotient by 2 again, and record the next remainder

4. Repeat until the quotient becomes 0

5. Write the remainders in reverse order - that’s your binary number

Example 1: Convert 13 to Binary

Binary = Reverse of remainders = 1101

 So, 13 (decimal) = 1101 (binary)

Example 2: Convert 45 to Binary

Binary = 101101

 So, 45 (decimal) = 101101 (binary)

 

Decimal to Binary Conversion Chart (1–20)

 

Applications of Decimal to Binary Conversion

• In Computer Programming
  • All modern programming languages ultimately convert code into binary for the processor to understand.
• In Digital Electronics
  • Microcontrollers and digital circuits operate using binary logic.
• In Networking
  • IP addresses, which are the addresses of our internet network and data packets ( data carrying method)  are handled as binary under the hood.
• In Competitive Exams     
  • Decimal to binary conversion is an essential concept in computer aptitude and reasoning sections.

 

Common Mistakes & Tips

 

Decimal to Binary Practice Problems

Instructions: Convert each decimal number to its binary equivalent. Show your steps clearly using the division-by-2 method.

Easy Level

1. Convert 5 to binary.

2. Convert 9 to binary.

3. Convert 12 to binary.

4. Convert 15 to binary.

5. Convert 18 to binary.

Intermediate Level

6. Convert 25 to binary.

7. Convert 37 to binary.

8. Convert 50 to binary.

9. Convert 63 to binary.

10. Convert 75 to binary.

Advanced Level

11. Convert 100 to binary.

12. Convert 128 to binary.

13. Convert 156 to binary.

14. Convert 200 to binary.

15. Convert 255 to binary.

Challenge Section

16. Convert 512 to binary.

17. Convert 768 to binary.

18. Convert 1023 to binary.

19. Convert 2048 to binary.

20. Convert 4096 to binary.

Decimal to Binary Converter Examples

Below are detailed examples showing how the decimal to binary converter works using the division-by-2 method.

Example 1: Convert 5 to Binary

Step 1: 5 ÷ 2 = 2, remainder = 1
Step 2: 2 ÷ 2 = 1, remainder = 0
Step 3: 1 ÷ 2 = 0, remainder = 1
Binary = 101 (Write remainders in reverse order)

Example 2: Convert 9 to Binary

Step 1: 9 ÷ 2 = 4, remainder = 1
Step 2: 4 ÷ 2 = 2, remainder = 0
Step 3: 2 ÷ 2 = 1, remainder = 0
Step 4: 1 ÷ 2 = 0, remainder = 1
Binary = 1001

Example 3: Convert 25 to Binary

Step 1: 25 ÷ 2 = 12, remainder = 1
Step 2: 12 ÷ 2 = 6, remainder = 0
Step 3: 6 ÷ 2 = 3, remainder = 0
Step 4: 3 ÷ 2 = 1, remainder = 1
Step 5: 1 ÷ 2 = 0, remainder = 1
Binary = 11001 

Example 4: Convert 100 to Binary

Step 1: 100 ÷ 2 = 50, remainder = 0
Step 2: 50 ÷ 2 = 25, remainder = 0
Step 3: 25 ÷ 2 = 12, remainder = 1
Step 4: 12 ÷ 2 = 6, remainder = 0
Step 5: 6 ÷ 2 = 3, remainder = 0
Step 6: 3 ÷ 2 = 1, remainder = 1
Step 7: 1 ÷ 2 = 0, remainder = 1
Binary = 1100100

 

Real-life Usage

Scenario: Digital Image Storage

Let’s say you take a photo using your smartphone. Each pixel in that photo is stored using numbers, and these numbers represent colors. Suppose one pixel has a grayscale value of 200 in decimal.

To store this information digitally, your phone needs to convert that decimal number (200) into binary, because computers only understand binary (0s and 1s). 

 

Conclusion

Decimal to Binary is a required part to know in maths. Basically, these are two different number systems. Converting decimal numbers to binary is not just a classroom skill — it's a foundational tool in technology and engineering. Number system clears out the computer language problems easily. By learning simple methods and practicing regularly, you’ll master this essential concept with ease. Whether you're preparing for exams, coding in Python, or exploring computer science, this guide will help you every step of the way.

 

Related Links

• Like, Unlike Decimals and Ordering of Decimals for Class 4

• Convert Paise Into Rupees

Frequently Asked Questions (FAQs)

 

1.Why do we convert decimal to binary?

As computers understand only binary (0s and 1s), so decimal numbers need to be converted for processing and storage. 

2.What is the binary of 100?

Divide repeatedly by 2:

• 100 ÷ 2 = 50, R = 0

• 50 ÷ 2 = 25, R = 0

• 25 ÷ 2 = 12, R = 1

• 12 ÷ 2 = 6, R = 0

• 6 ÷ 2 = 3, R = 0

• 3 ÷ 2 = 1, R = 1

• 1 ÷ 2 = 0, R = 1
  
  

Reverse remainders: 1100100

So, 100 (decimal) = 1100100 (binary)

3.What careers use binary conversions?

• Software Engineering

• Data Science

• Electronics Engineering

• Network Security

• Robotics and Automation 

4.What is the binary of a decimal with a fractional part?

For decimal fractions (like 12.625), convert the integer and fractional parts separately.

• 12 = 1100

• 0.625 = (0.101)₂ (multiply by 2 repeatedly)

So, 12.625 = 1100.101

Explore More Number System Conversions with Orchids International School!