Decimal to Binary Numbers

Introduction

Decimal to binary number conversion is like translating a number from our everyday counting system (base 10) into the computer’s language (base 2). In binary, you only have two digits (0 and 1), but you can still represent any number using the combination of these two digits. For example, the decimal number 12 becomes 1100 in binary. Just like we learn to say “hello” in different languages, we can also change numbers from one number system to another, such as from decimal to binary or octal (base 8) or hexadecimal (base 16). Once you learn the steps, converting decimal to binary feels simple – and there are online tools to make it even easier. Further, let’s learn more about decimal to binary number conversion!

 

Table of Contents

• Decimal to Binary Number
• 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 & Real-Life Usage
• Common Mistakes & Tips
• Decimal to Binary Converter Examples
• Decimal to Binary Practice Problems
• Conclusion
• FAQs on Decimal to Binary Numbers

Decimal to Binary Number :

It is the process of changing a number from base 10 (decimal) to base 2 (binary). Binary numbers, made of only 0 and 1, are used in computers for coding and processing because computers understand only binary language.

Decimal Number System:
This is the number system we use every day, based on 10 digits (0–9). Each place value is 10 times bigger than the one to its right. Examples: 2130, 2850. If no base is mentioned, we assume it’s decimal.

Binary Number System:
Used mainly in computers, it has only two digits: 0 and 1. Each digit is called a bit. The leftmost bit is the Most Significant Bit (MSB) and the rightmost is the Least Significant Bit (LSB). Examples: 1110, 1001.

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.

 

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 & Real-life Usage : 

• 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.

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). 

 

Common Mistakes & Tips

 

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

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 7 to binary.
2. Convert 10 to binary.
3. Convert 14 to binary.
4. Convert 20 to binary.
5. Convert 25 to binary.

Intermediate Level

1. Convert 28 to binary.
2. Convert 42 to binary.
3. Convert 55 to binary.
4. Convert 68 to binary.
5. Convert 80 to binary.

Advanced Level

1. Convert 90 to binary.
2. Convert 135 to binary.
3. Convert 170 to binary.
4. Convert 220 to binary.
5. Convert 300 to binary.

Challenge Section

1. Convert 3072 to binary.
2. Convert 5000 to binary.
3. Convert 8191 to binary.
4. Convert 10000 to binary.
5. Convert 16384 to binary.

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.

 

Frequently Asked Questions on Decimal to Binary Numbers

 

1. Why do we convert decimal to binary?

Ans: 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?

Ans: 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?

Ans:

• Software Engineering

• Data Science

• Electronics Engineering

• Network Security

• Robotics and Automation 

 

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

Ans: 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!