Number Base Converter
Type in any field to convert instantly across all bases.
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
- Web Colors: HTML colors are 24-bit codes.
#FF5733means Red=255 (FF), Green=87 (57), Blue=51 (33). - Memory Addresses: Computer RAM is addressed in Hex (e.g., 0x00400000) to keep numbers manageable.
- ASCII & Unicode: Text characters are stored as numbers (e.g., 'A' is 65 decimal or 0x41 hex).
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...)