Base Converter – Binary, Decimal, Octal, Hexadecimal Calculator

In computer science, mathematics, and electronics, converting numbers between different bases is essential. Whether it’s binary (base 2), decimal (base 10), octal (base 8), or hexadecimal (base 16), the Base Converter simplifies calculations and prevents errors. This tool is ideal for students, programmers, and engineers.

Why Base Conversion Is Important

• Computer Programming: Binary and hexadecimal are core to coding and memory addresses.
• Digital Electronics: Octal and binary simplify circuit design.
• Education: Helps students understand number systems and their relationships.
• Mathematics: Enables easy calculation in different bases for algorithms and problem-solving.

Base Conversion Formulas

Here are the common formulas and methods for base conversion:

Conversion Type	Formula / Method	Example
Decimal → Binary	Divide the decimal number by 2 repeatedly and write remainders from bottom to top.	Decimal 13 → Binary 1101
Decimal → Octal	Divide the decimal number by 8 repeatedly and write remainders from bottom to top.	Decimal 65 → Octal 101
Decimal → Hexadecimal	Divide the decimal number by 16 repeatedly and write remainders from bottom to top. Use A-F for 10-15.	Decimal 254 → Hexadecimal FE
Binary → Decimal	Multiply each bit by 2ⁿ, where n is the position from right (starting at 0), then sum.	Binary 1011 → Decimal 11
Octal → Decimal	Multiply each digit by 8ⁿ, where n is position from right, then sum.	Octal 17 → Decimal 15
Hexadecimal → Decimal	Multiply each digit by 16ⁿ, sum all (A=10, B=11, …, F=15).	Hexadecimal 1A → Decimal 26

How the Base Converter Works

1. Select the source base (Binary, Decimal, Octal, Hexadecimal).
2. Enter the number you want to convert.
3. Select the target base for conversion.
4. The converter applies the corresponding formula and instantly provides the result.

Step-by-Step Example 1: Decimal to Binary

Problem: Convert decimal 23 to binary.
Solution:

• 23 ÷ 2 = 11 remainder 1
• 11 ÷ 2 = 5 remainder 1
• 5 ÷ 2 = 2 remainder 1
• 2 ÷ 2 = 1 remainder 0
• 1 ÷ 2 = 0 remainder 1

Reading remainders from bottom to top: 10111
Result: Decimal 23 = Binary 10111

Step-by-Step Example 2: Hexadecimal to Decimal

Problem: Convert hexadecimal 2F to decimal.
Solution:

• 2 × 16¹ = 32
• F (15) × 16⁰ = 15

Sum = 32 + 15 = 47
Result: Hex 2F = Decimal 47

Step-by-Step Example 3: Binary to Octal

Problem: Convert binary 110101 to octal.
Solution:

• Group binary digits in sets of 3 from right: 110 101
• 110 = 6, 101 = 5

Result: Binary 110101 = Octal 65

FAQs – Base Converter

1. What is the difference between binary, octal, decimal, and hexadecimal?
Binary uses base 2, octal base 8, decimal base 10, and hexadecimal base 16.

2. Can this converter handle fractional numbers?
Some converters support fractions; standard method involves multiplying by base for fractional part.

3. Do I need to know formulas to use it?
No, the converter applies all formulas automatically; you only input the number.

4. Is it suitable for students and programmers?
Yes, it’s ideal for homework, exams, coding, and electronics projects.

5. Can it convert between any combination of bases?
Yes, you can convert between Binary, Octal, Decimal, and Hexadecimal freely.

6. Can I convert large numbers?
Yes, the converter supports very large numbers.

7. Is it mobile-friendly?
Yes, it works perfectly on smartphones, tablets, and desktop browsers.

8. Can I use it for negative numbers?
Yes, negative numbers can also be converted between bases.

9. Are letters A-F case-sensitive in hexadecimal input?
No, both uppercase and lowercase letters are accepted.

10. Is this tool free?
Yes, it’s completely free and online.