Number Base Converter

Type in any field to convert instantly across all bases.

Decimal (Base 10) DEC
Invalid Decimal
Binary (Base 2) BIN
Invalid Binary (0-1 only)
Hexadecimal (Base 16) HEX
Invalid Hex (0-9, A-F only)
Octal (Base 8) OCT
Invalid Octal (0-7 only)

Why do we need different bases?

Humans count in Decimal (Base 10) because we have 10 fingers. Computers, built on switches (transistors), can only understand "On" or "Off." This forces them to use Binary (Base 2).

However, binary is hard for humans to read (e.g., 11010011). Hexadecimal (Base 16) is a shorthand for binary, where every 4 bits = 1 Hex digit. It is the bridge between human and machine logic.

Conversions Explained

Binary to Decimal (Base 2 -> 10)

Each position represents a power of 2. For 101: (1×4) + (0×2) + (1×1) = 5.

Hex to Binary (Base 16 -> 2)

Convert each Hex digit to its 4-bit binary equivalent. e.g., A5:
A (10) = 1010
5 = 0101
Result: 10100101

Practical Applications

FAQ

What is Octal (Base 8)?

Octal uses digits 0-7. It was popular in early computing (like the PDP-11) because 3 bits = 1 Octal digit. Today, it is mostly seen in Linux File Permissions (e.g., chmod 755).

What is "Two's Complement"?

It is how computers store negative numbers. To make a number negative, you flip all bits and add 1. This allows standard addition hardware to handle subtraction automatically.

How do I count in Binary on my fingers?

Each finger is a bit. Thumb=1, Index=2, Middle=4, Ring=8, Pinky=16. You can count up to 31 on one hand! (Just be careful with the number 4...)