Binary to Decimal Converter
Convert between binary, decimal, hexadecimal, and octal number systems.
Result
Binary
Decimal
Hexadecimal
Octal
How It Works
Enter a number in any base (binary, decimal, hex, or octal) and see it instantly converted to all other bases with step-by-step working.
**Binary to Decimal Converter — Master Number Base Conversion**
Computers speak in binary (base 2). Humans prefer decimal (base 10). Hexadecimal (base 16) bridges the two for programmers. Our multi-base converter handles all four common number systems with full step-by-step workings.
**The Four Number Bases**
**Binary (Base 2)**
Digits: 0, 1
Used by: Computer hardware, digital logic, low-level programming
**Octal (Base 8)**
Digits: 0–7
Used by: Unix file permissions (chmod 755), some legacy systems
**Decimal (Base 10)**
Digits: 0–9
Used by: Everyday human counting
**Hexadecimal (Base 16)**
Digits: 0–9, A–F (A=10, B=11, C=12, D=13, E=14, F=15)
Used by: Colour codes (#FF5733), memory addresses, debugging
**Conversion Method: Binary to Decimal**
Each binary digit represents a power of 2, from right to left:
1011₂ = 1×2³ + 0×2² + 1×2¹ + 1×2⁰
= 8 + 0 + 2 + 1 = 11₁₀
**Conversion Method: Decimal to Binary**
Repeated division by 2:
11 ÷ 2 = 5 remainder 1
5 ÷ 2 = 2 remainder 1
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1
Read remainders from bottom to top: 1011
**Hex and RGB Colours**
The hex colour #FF5733 means:
- FF = 255 (red), 57 = 87 (green), 33 = 51 (blue)
This is RGB(255, 87, 51) — an orange-red colour.
**Binary in Computing**
- 1 bit = one binary digit (0 or 1)
- 8 bits = 1 byte (values 0–255)
- 16 bits = 1 word (0–65,535)
- 32 bits = 0–4,294,967,295
- 64 bits = modern computing standard