How to Convert Decimal to Binary — Easy Method with Examples

Introduction

Converting decimal to binary is one of the most common tasks in computer science education. Every BCA, BTech, and diploma student must learn this conversion for exams, lab practicals, and understanding how computers store numbers. This guide teaches you the standard division-by-2 method with clear, worked examples.

Binary (base 2) is the language computers understand — every number, character, and instruction is ultimately stored as a sequence of 0s and 1s. Understanding how decimal maps to binary is the first step to grasping digital systems.

🔧 Try it now: Decimal to Binary Converter — paste any number and get binary output instantly with full working.

The Method: Repeated Division by 2

To convert any decimal (base 10) number to binary (base 2):

1. Divide the decimal number by 2
2. Write down the remainder (0 or 1)
3. Use the quotient as the new number
4. Repeat until the quotient becomes 0
5. Read all remainders from bottom to top — that is your binary result

Worked Examples

Example 1: Convert 13 to Binary

Step	Division	Quotient	Remainder
1	13 ÷ 2	6	1
2	6 ÷ 2	3	0
3	3 ÷ 2	1	1
4	1 ÷ 2	0	1

Read remainders bottom to top: 1101₂

Verification: 1×8 + 1×4 + 0×2 + 1×1 = 8+4+0+1 = 13 ✓

Example 2: Convert 25 to Binary

Step	Division	Quotient	Remainder
1	25 ÷ 2	12	1
2	12 ÷ 2	6	0
3	6 ÷ 2	3	0
4	3 ÷ 2	1	1
5	1 ÷ 2	0	1

Read remainders bottom to top: 11001₂

Example 3: Convert 100 to Binary

Step	Division	Quotient	Remainder
1	100 ÷ 2	50	0
2	50 ÷ 2	25	0
3	25 ÷ 2	12	1
4	12 ÷ 2	6	0
5	6 ÷ 2	3	0
6	3 ÷ 2	1	1
7	1 ÷ 2	0	1

Read remainders bottom to top: 1100100₂

Example 4: Convert 255 to Binary

255 ÷ 2 = 127 R1, 127 ÷ 2 = 63 R1, 63 ÷ 2 = 31 R1, 31 ÷ 2 = 15 R1, 15 ÷ 2 = 7 R1, 7 ÷ 2 = 3 R1, 3 ÷ 2 = 1 R1, 1 ÷ 2 = 0 R1

Result: 11111111₂ (eight 1s — one full byte, the maximum 8-bit unsigned value)

Quick Reference: Common Decimal-Binary Values

Decimal	Binary
0	0
1	1
5	101
10	1010
16	10000
32	100000
64	1000000
128	10000000
255	11111111

Common Mistakes

1. Reading remainders top to bottom — Always read from the last remainder to the first
2. Stopping too early — Keep dividing until the quotient reaches 0
3. Arithmetic errors in division — Double-check each step, especially for large numbers
4. Forgetting leading zeros — In 8-bit representation, decimal 5 is 00000101, not just 101

When Do You Use This?

• Computer science exams (BCA, BTech, GATE, university)
• Understanding memory addresses and register values
• Debugging binary data and network protocols
• Programming bitwise operations
• Digital logic design and truth tables

Try It Online

Use the free Number System Converter on Numverto to instantly convert any decimal number to binary (plus octal and hex). The tool shows complete step-by-step division working so you can verify your manual calculations.

Frequently Asked Questions

What is the binary equivalent of decimal 10?

Decimal 10 in binary is 1010. Using the division method: 10÷2=5 R0, 5÷2=2 R1, 2÷2=1 R0, 1÷2=0 R1. Read bottom-up: 1010.

How many binary digits does a number need?

The number of bits needed is ⌈log₂(n+1)⌉. For example, 255 needs 8 bits, 256 needs 9 bits, and 1000 needs 10 bits.

What is decimal 0 in binary?

Decimal 0 is simply 0 in binary. In 8-bit representation, it is written as 00000000.

Can I convert decimal fractions to binary?

Yes, but the method differs. For the fractional part, multiply by 2 repeatedly and note the integer parts (read top to bottom). This guide covers whole numbers; use our converter for fractional values.

Why is this method called “repeated division”?

Because you repeatedly divide the number by the target base (2 for binary) until you reach zero, collecting remainders at each step. The same approach works for converting to any base — divide by 8 for octal, by 16 for hex.