Number Base Converter

Number base conversion is a fundamental skill in computer science and digital electronics. Our free number base converter instantly translates values between binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16).

**The Four Number Bases**

**Binary (Base 2)** uses only 0 and 1. It is the foundation of all digital computing — every piece of data in a computer is ultimately stored as binary. Understanding binary is essential for bitwise operations, low-level programming, and computer architecture.

**Octal (Base 8)** uses digits 0–7. It was historically used in computing because each octal digit maps exactly to 3 binary digits, making binary more readable. Unix file permissions (like chmod 755) are expressed in octal.

**Decimal (Base 10)** is the familiar number system we use in everyday life, using digits 0–9. All standard arithmetic and most programming languages default to decimal for numeric literals.

**Hexadecimal (Base 16)** uses digits 0–9 and letters A–F. Each hex digit maps to exactly 4 binary digits (nibble), making it compact for representing binary data. Used extensively for: memory addresses, color codes (#FF5733), byte values, and CPU instructions.

**Real-World Applications**

- **Color codes**: `#1A2B3C` = R:26, G:43, B:60 in decimal
- **Memory addresses**: `0x7FFF5FBF8000` in hexadecimal
- **File permissions**: `chmod 755` = binary 111 101 101
- **Bitwise operations**: easier to visualize in binary
- **Network masks**: subnet masks shown in binary

**Conversion Tips**

To convert binary to hex, group binary digits in sets of 4 from the right and convert each group. To convert decimal to any base, repeatedly divide by the target base and collect remainders.

**Privacy**

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