technology ToolUpdated 2026-09-19
Binary to Decimal Converter
Convert binary code (base 2) into standard decimal integers (base 10) with positional power-of-2 breakdowns.
Formula & Mathematical Methodology
Decimal = Σ(bit × 2ⁿ)
Multiply each binary digit by 2 raised to its positional index (starting at 0 from the right).
How to Use This Binary to Decimal Converter
- Enter any binary string composed of 1s and 0s.
Step-by-Step Worked Example
Scenario: Convert 110101₂ to decimal
1. 1 × 2⁵ (32) = 32
2. 1 × 2⁴ (16) = 16
3. 0 × 2³ (8) = 0
4. 1 × 2² (4) = 4
5. 0 × 2¹ (2) = 0
6. 1 × 2⁰ (1) = 1
7. Sum: 32 + 16 + 0 + 4 + 0 + 1 = 53
Final Calculated Result: 53
What Does Your Result Mean?
Presents human-readable decimal values from raw bit streams.
Common Practical Applications:
- Interpreting microprocessor registers
- IP address octet conversion
Important Limitations & Assumptions:
- Invalid non-binary characters will produce an input validation error.
Frequently Asked Questions
What is the largest decimal number you can represent in 8 bits?
An 8-bit unsigned binary number (11111111) represents 255 (2⁸ − 1).
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