Decimal to Binary Converter - Free Online Tool with Calculator & Table

Convert decimal to binary instantly with our professional decimal to binary converter. Features decimal to binary table, conversion examples in Python, Java, C++, and step-by-step algorithm explanation. Perfect decimal to binary calculator for programmers and students.

Master how to convert decimal to binary with comprehensive decimal to binary conversion examples, programming code samples, and complete conversion tables. Learn the decimal to binary conversion formula and practice with real examples including convert decimal to binary for numbers like 13, 25, 255, and more.

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How to Convert Decimal to Binary - Division by 2 Method

Decimal to Binary Conversion Formula & Algorithm

Repeatedly divide by 2, record remainders, then reverse the order
Decimal ÷ 2 = Quotient + Remainder (0 or 1)

The decimal to binary conversion algorithm works by repeatedly dividing the decimal number by 2 and recording each remainder (0 or 1). The binary representation is formed by reading the remainders in reverse order. This method is the most reliable way to convert decimal to binary numbers.

Decimal to Binary Conversion Examples: Convert 13 to Binary

13 ÷ 2 = 6 remainder 1

6 ÷ 2 = 3 remainder 0

3 ÷ 2 = 1 remainder 1

1 ÷ 2 = 0 remainder 1

Remainder sequence: 1, 0, 1, 1

Reverse order: 1101 (binary)

Therefore, decimal 13 converts to binary 1101

Verification Method - Binary to Decimal Check

Convert binary 1101 back to decimal:

1×2³ + 1×2² + 0×2¹ + 1×2⁰

= 8 + 4 + 0 + 1

= 13 ✓ (matches original)

Always verify your decimal to binary conversion using positional notation

Complete Decimal to Binary Table & Conversion Examples

Decimal to Binary Table - 4-bit Values (0-15)

Decimal	Binary	Hex
0	0000	0
1	0001	1
2	0010	2
3	0011	3
4	0100	4
5	0101	5
6	0110	6
7	0111	7
8	1000	8
9	1001	9
10	1010	A
11	1011	B
12	1100	C
13	1101	D
14	1110	E
15	1111	F

Essential decimal to binary table for quick reference and manual calculations

Common Decimal to Binary Conversion Examples

Decimal	Binary	Description
25	11001	5-bit number
50	110010	6-bit number
100	1100100	7-bit number
128	10000000	8-bit power of 2
255	11111111	8-bit all 1s
256	100000000	9-bit power of 2
512	1000000000	10-bit power of 2
1024	10000000000	11-bit power of 2
2048	100000000000	12-bit power of 2
65535	1111111111111111	16-bit all 1s

Popular decimal numbers and their binary equivalents for programming reference

Decimal to Binary Programming Examples & Code

🐍Python - Decimal to Binary Conversion

# Method 1: Using bin() function

decimal = 13

binary = bin(decimal)[2:] # Remove '0b' prefix

print(binary) # Output: 1101

# Method 2: Manual algorithm

def decimal_to_binary(n):

if n == 0: return "0"

binary = ""

while n > 0:

binary = str(n % 2) + binary

n = n // 2

return binary

Python provides built-in bin() function and manual implementation for decimal to binary conversion

🟨JavaScript - Decimal to Binary Conversion

const decimal = 13;

const binary = decimal.toString(2);

console.log(binary);

function decimalToBinary(n) {

if (n === 0) return "0";

let binary = "";

while (n > 0) {

binary = (n % 2) + binary;

n = Math.floor(n / 2);

}

return binary;

}

JavaScript toString(2) method and manual implementation for decimal to binary conversion

☕Java - Decimal to Binary Conversion

int decimal = 13;

String binary = Integer.toBinaryString(decimal);

System.out.println(binary);

public static String decimalToBinary(int n) {

if (n == 0) return "0";

StringBuilder binary = new StringBuilder();

while (n > 0) {

binary.insert(0, n % 2);

n = n / 2;

}

return binary.toString();

}

Java Integer.toBinaryString() method and manual implementation

🔧C++ - Decimal to Binary Conversion

#include <bitset>

#include <iostream>

int decimal = 13;

std::bitset<8> binary(decimal);

std::cout << binary << std::endl;

std::string decimalToBinary(int n) {

if (n == 0) return "0";

std::string binary = "";

while (n > 0) {

binary = (n % 2 ? "1" : "0") + binary;

n /= 2;

}

return binary;

}

C++ bitset library and manual algorithm for decimal to binary conversion

Mathematical Foundation of Decimal to Binary Conversion

Why Decimal to Binary Conversion Works

Decimal to binary conversion is based on the fundamental principle that any number can be represented as a sum of powers of 2. The binary number system uses base 2, where each position represents a power of 2, starting from 2⁰ = 1 on the rightmost position.

Power of 2 Table for Decimal to Binary Conversion:

2⁰ = 1

2¹ = 2

2² = 4

2³ = 8

2⁴ = 16

2⁵ = 32

2⁶ = 64

2⁷ = 128

2⁸ = 256

2⁹ = 512

2¹⁰ = 1024

2¹¹ = 2048

Step-by-Step: 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

Reading remainders from bottom to top:

25 (decimal) = 11001 (binary)

Verification: Binary 11001 to Decimal

Position: 4 3 2 1 0

Binary: 1 1 0 0 1

Power: 16 8 4 2 1

1×16 + 1×8 + 0×4 + 0×2 + 1×1

= 16 + 8 + 0 + 0 + 1

= 25 ✓ (matches original)

Practical Applications of Decimal to Binary Conversion

Computer Programming

Decimal to binary conversion is essential for bitwise operations, memory management, and understanding how computers store and process data at the hardware level.

Digital Electronics

Binary representation is fundamental in digital circuits, logic gates, and electronic systems where only two states (0 and 1) can exist.

Network Addressing

IP addresses and subnet masks require decimal to binary conversion for network configuration and understanding CIDR notation.

Data Compression

Binary representation is crucial for compression algorithms and understanding how data is encoded and stored efficiently.

Related Number System Conversion Tools

Binary to Decimal

Convert binary numbers back to decimal with our binary to decimal converter and table.

Hex to Binary

Convert hexadecimal numbers to binary with our hexadecimal to binary converter.

Hex to Decimal

Convert hexadecimal numbers to decimal format with our hex to decimal tool.

Popular Decimal to Binary Conversion Examples & Hexadecimal Connection

Frequently Searched Decimal to Binary Conversions

Convert 17 to Binary

17 ÷ 2 = 8 remainder 1

8 ÷ 2 = 4 remainder 0

4 ÷ 2 = 2 remainder 0

2 ÷ 2 = 1 remainder 0

1 ÷ 2 = 0 remainder 1

Result: 10001

Convert 15 to Binary

15 ÷ 2 = 7 remainder 1

7 ÷ 2 = 3 remainder 1

3 ÷ 2 = 1 remainder 1

1 ÷ 2 = 0 remainder 1

Result: 1111

Convert 31 to Binary

31 ÷ 2 = 15 remainder 1

15 ÷ 2 = 7 remainder 1

7 ÷ 2 = 3 remainder 1

3 ÷ 2 = 1 remainder 1

1 ÷ 2 = 0 remainder 1

Result: 11111

Decimal to Binary and Hexadecimal Connection

Understanding the relationship between decimal, binary, and hexadecimal number systems is crucial for programming and digital electronics. Each hexadecimal digit represents exactly 4 binary digits (bits), making conversions between these systems efficient.

Decimal	Binary (4-bit)	Hexadecimal	Common Use
10	1010	A	Line feed (LF)
13	1101	D	Carriage return (CR)
16	10000	10	Power of 2
32	100000	20	Space character
64	1000000	40	At symbol (@)
127	1111111	7F	DEL character
255	11111111	FF	8-bit max value

This table shows how decimal to binary conversion relates to hexadecimal representation, essential for programming and computer science.

Tips for Decimal to Binary Conversion & Common Mistakes

✅ Best Practices

•Always read remainders from bottom to top when using division method
•Verify your result by converting binary back to decimal
•Use powers of 2 table for quick mental calculations
•Practice with common numbers like 255, 256, 1024

❌ Common Mistakes

•Reading remainders in the wrong order (top to bottom instead of bottom to top)
•Forgetting to include leading zeros when working with fixed-width binary
•Not verifying the result with reverse conversion
•Mixing up the division by 2 method with other base conversions