Binary โ Decimal Converter
Convert between binary and decimal number systems instantly
๐ Binary โ Decimal Conversion Details
Binary to Decimal Formula
Sum each binary digit multiplied by 2 raised to its position power (from right, starting at 0).
Decimal to Binary Formula
Repeatedly divide decimal by 2, collect remainders in reverse order.
Binary System Basics
Binary uses only two digits: 0 and 1.
- Base-2 number system
- Each digit is called a "bit"
- 8 bits = 1 byte
- Used in all digital systems
Decimal System Basics
Decimal uses ten digits: 0-9.
- Base-10 number system
- Most common number system
- Used in everyday counting
- Each position is power of 10
๐ข Step-by-Step Calculation
Positions from right (starting at 0):
1(2โต) + 0(2โด) + 1(2ยณ) + 0(2ยฒ) + 1(2ยน) + 0(2โฐ)
= 32 + 0 + 8 + 0 + 2 + 0 = 42โโ
๐ Common Binary Values
| Binary | Decimal | Hex | Power of 2 |
|---|---|---|---|
| 1 | 1 | 0x1 | 2โฐ |
| 10 | 2 | 0x2 | 2ยน |
| 100 | 4 | 0x4 | 2ยฒ |
| 1000 | 8 | 0x8 | 2ยณ |
| 1111 | 15 | 0xF | - |
| 11111111 | 255 | 0xFF | - |
| 1111111111111111 | 65535 | 0xFFFF | - |
โ Frequently Asked Questions
A: Binary is a base-2 number system that uses only two digits: 0 and 1. It's the fundamental language of computers and digital systems.
A: Multiply each binary digit by 2 raised to its position power (starting from right with position 0), then sum all results.
A: This converter supports up to 32-bit binary numbers (max decimal: 4,294,967,295).
A: Yes! This is a bidirectional converter. Type in the decimal field to get binary, or type in the binary field to get decimal.