Binary To Decimal
This Binary to Decimal Converter transforms binary numbers (base-2) into decimal (base-10) instantly. Enter binary digits (e.g., 1101), and the tool calculates the decimal equivalent. Free, no installation needed. Essential for programmers, students, and engineers working with digital systems, networking, or computer science projects.
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How to Convert Binary to Decimal: A Step-by-Step Guide
Binary (base-2) and decimal (base-10) are fundamental number systems in computing. Converting binary to decimal is essential for programming, networking, and digital electronics. Here’s how to do it manually and with tools:
Manual Conversion: The Positional Weight Method
Write down the binary number (e.g., 1101).
Assign powers of 2 to each digit, starting from the right (LSB → MSB):
Rightmost digit: 20=120=1
Next: 21=221=2
Next: 22=422=4
Leftmost digit: 23=823=8
Multiply each digit by its power of 2:
text
1 → 1 × 8 = 8 1 → 1 × 4 = 4 0 → 0 × 2 = 0 1 → 1 × 1 = 1
Sum the results: 8+4+0+1=138+4+0+1=13.
∴ 1101 in binary = 13 in decimal.
Binary to Decimal Conversion Table
| Binary | Decimal |
|---|---|
| 0000 | 0 |
| 0001 | 1 |
| 0010 | 2 |
| 0100 | 4 |
| 1000 | 8 |
| 1111 | 15 |
Fast Conversion: Use a Binary to Decimal Converter
For longer binary strings (e.g., 10101101), skip the math:
Online Tools: Use a binary to decimal converter or binary to decimal calculator.
How it works:
Enter your binary number.
Click “Convert” → Instantly get decimal results.
Real-World Applications
Programming: Debugging memory addresses.
Networking: Calculating IP subnets.
Electronics: Configuring microcontroller registers.
Try It Yourself!
Convert these:
1010 → ? (Answer: 10)
111000 → ? (Answer: 56)
Stuck? Use a binary to decimal calculator for instant verification!
Final Tip: Bookmark a trusted converter for on-the-fly conversions. Master both methods—manual for exams, tools for real tasks!