Binary to Decimal Converter
Convert binary (base-2) numbers to decimal (base-10) representation. Essential for understanding computer data representation.
Input (Binary)
Enter a binary number
Output (Decimal)
Decimal representation
What is Binary to Decimal Conversion?
Binary to decimal conversion transforms base-2 numbers (binary) into base-10 numbers (decimal). This is essential for understanding how computers represent and process numeric data.
How Binary Works
Binary uses only two digits: 0 and 1. Each position represents a power of 2.
Position Values (right to left):
- Position 0: 2^0 = 1
- Position 1: 2^1 = 2
- Position 2: 2^2 = 4
- Position 3: 2^3 = 8
- Position 4: 2^4 = 16
- And so on...
Conversion Process
To convert binary to decimal, multiply each digit by its position value and sum:
Example: 101010
- (1 × 32) + (0 × 16) + (1 × 8) + (0 × 4) + (1 × 2) + (0 × 1)
- = 32 + 0 + 8 + 0 + 2 + 0
- = 42
More Examples:
1111= 1510000000= 12811111111= 255
Common Use Cases:
- Understanding computer data representation
- Network subnet calculations
- Bit manipulation in programming
- Digital electronics
- Understanding machine code