Number Base Converter Online — Binary, Decimal, Hex, and Octal

What Are Number Bases?

A number base (or radix) determines how many unique digits are used to represent numbers. Humans use decimal (base 10, digits 0–9). Computers work natively in binary (base 2, digits 0–1). Hexadecimal (base 16, digits 0–9 plus A–F) is shorthand for binary, widely used in programming. Octal (base 8, digits 0–7) appears in Unix file permissions and older systems.

Understanding number base conversion is essential for low-level programming, network address calculations, cryptography, color representation in CSS (e.g., #FF5733 is hex), and interpreting system-level values.

How to Use a Number Base Converter

1. Enter the number in the source base field.
2. Select the source base — binary, octal, decimal, or hex.
3. View conversions — the tool shows the number in all four bases simultaneously.
4. Use the results — copy the converted value for use in your code or calculations.
5. For hex — input can use uppercase or lowercase letters (A–F or a–f).

Number Base Reference

Common Conversions Table

Decimal | Binary    | Hex | Octal
--------|-----------|-----|------
0       | 0000      | 0   | 0
1       | 0001      | 1   | 1
8       | 1000      | 8   | 10
10      | 1010      | A   | 12
15      | 1111      | F   | 17
16      | 0001 0000 | 10  | 20
255     | 1111 1111 | FF  | 377
256     | 0001 0000 0000 | 100 | 400

How Hex Colors Work

CSS hex colors (#RRGGBB) represent red, green, and blue channels as two hex digits each. #FF0000 is pure red (R=255, G=0, B=0). #FFFFFF is white (all channels at 255). Converting hex to decimal reveals the actual 0–255 channel values.

Use Cases

Bitwise Operations in Programming

Bitwise operations (AND, OR, XOR, shifts) are much easier to visualize in binary. When debugging bitmask logic, convert the decimal values to binary to see which bits are set. Convert back to check the result.

Network Address Calculations

IPv4 addresses and subnet masks are often expressed in decimal but work as 32-bit binary numbers. Understanding binary helps calculate network and broadcast addresses, subnet sizes, and CIDR notation. /24 subnet = 8 host bits = 256 addresses.

CSS Color Values

Converting between hex colors and decimal RGB values helps when you need to programmatically manipulate colors — calculate complementary colors, adjust brightness, or convert to HSL for CSS filters.

Frequently Asked Questions

Why do programmers use hexadecimal?

Hexadecimal is a compact way to represent binary data. One hex digit represents exactly 4 bits; two hex digits represent one byte (8 bits). This makes hex much more readable than long binary strings while maintaining a direct mapping. Memory addresses, color values, and byte sequences are conventionally expressed in hex.

How do I convert binary to decimal manually?

Each binary digit represents a power of 2. From right to left: position 0 = 2^0 = 1, position 1 = 2^1 = 2, position 2 = 2^2 = 4, etc. Multiply each bit by its position value and sum: 1010 = 1×8 + 0×4 + 1×2 + 0×1 = 10 decimal.

What does the 0x prefix mean in code?

0x is the prefix used in most programming languages to indicate a hexadecimal literal. 0xFF equals 255 decimal. Similarly, 0b is the binary prefix in Python and many languages: 0b1111 equals 15 decimal.

How do negative numbers work in binary?

Most computers use two's complement to represent negative integers. To negate a number: invert all bits, then add 1. In an 8-bit system, -1 is represented as 11111111 (0xFF). This explains why a signed 8-bit integer ranges from -128 to 127.

What is octal used for in programming?

Octal appears most commonly in Unix/Linux file permissions. The permission chmod 755 uses octal: 7 = rwx (4+2+1), 5 = r-x (4+0+1). In Python, octal literals use the 0o prefix: 0o755. In C, a leading zero indicates octal: 0755.