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Binary to Decimal Converter
Convert binary numbers (Base 2) to decimal numbers (Base 10) with detailed mathematical explanations.
Binary to Decimal Calculator
Decimal Value (Base 10)
42
Mathematical Expansion
To convert a binary number to decimal, multiply each digit by the power of 2 corresponding to its position (starting at 0 on the far right):
1. Formula:
(1 × 2^5) + (0 × 2^4) + (1 × 2^3) + (0 × 2^2) + (1 × 2^1) + (0 × 2^0)
2. Intermediate terms:
32 + 0 + 8 + 0 + 2 + 0
3. Final Sum:
42
How to convert binary to decimal manually
The decimal number system we use in everyday life is a base-10 positional system, which means each position represents a power of 10. The binary system is a base-2 positional system, where each slot represents a power of 2.
To translate manually:
- Write down the binary number.
- Assign powers of 2 to each bit starting from right to left, beginning with 2^0 (which equals 1), then 2^1 (2), 2^2 (4), 2^3 (8), etc.
- Multiply each bit (0 or 1) by its corresponding power of 2.
- Add all the results together to find the final decimal value.
For example, 1101 is: (1 × 2^3) + (1 × 2^2) + (0 × 2^1) + (1 × 2^0) = 8 + 4 + 0 + 1 = 13.