Binary Converter
Why Do Computers Speak Binary?
Humans use the Decimal System (Base 10) because we have ten fingers. It feels natural to count 0, 1, 2... 9, and then rollover to 10.
Computers, however, don't have fingers. They are made of electrical switches (transistors). A switch only has two states: ON (1) or OFF (0).
This is why the Binary System (Base 2) is the fundamental language of technology. Every photo you see, every email you send, and even this webpage, is ultimately broken down into a massive stream of ones and zeros that your processor decodes at lightning speed.
How to Read Binary (The Doubling Rule)
Binary might look random, but it follows a strict pattern of doubling values from right to left.
In Decimal, column values are: 100s, 10s, 1s.
In Binary, column values are: 128, 64, 32, 16, 8, 4, 2, 1.
• The 8 bit is ON (1)
• The 4 bit is OFF (0)
• The 2 bit is ON (1)
• The 1 bit is ON (1)
Total: 8 + 0 + 2 + 1 = 11
Why Use Hexadecimal (Hex)?
Binary code gets extremely long, extremely fast. Writing the number "15" takes four digits in binary (1111), but only two in decimal.
To fix this, programmers use Hexadecimal (Base 16). It counts from 0 to 9, then uses letters A to F for 10 to 15.
- A = 10
- B = 11
- F = 15 (Maximum single digit value)
Hexadecimal is famously used for Web Colors (e.g., #FFFFFF for white) because it can compress long strings of binary into short, readable codes.
Common Conversions Chart
| Decimal | Binary | Hexadecimal |
|---|---|---|
| 0 | 0000 | 0 |
| 1 | 0001 | 1 |
| 5 | 0101 | 5 |
| 10 | 1010 | A |
| 15 | 1111 | F |
| 255 | 11111111 | FF |