Binary to Decimal Converter
🔢 Binary to Decimal Converter
Convert Binary ↔ Decimal Numbers Instantly — Free Online Tool
📖 How to Use the Binary ↔ Decimal Converter — Complete Guide
🎯 Why Convert Between Binary and Decimal?
Binary (base‑2) is the language of computers, while decimal (base‑10) is the language of humans. Converting between the two is fundamental for understanding how data is stored, IP addressing, subnetting, digital logic, and low‑level programming. For example, the binary number 1101 equals decimal 13 because (1×8)+(1×4)+(0×2)+(1×1) = 13.
📟 Binary → Decimal
- Click the "Binary → Decimal" tab.
- Enter a binary number using only 0 and 1. You can also input fractional binary like
101.11. - The decimal equivalent appears instantly in the dark output box, along with the step‑by‑step formula.
- Click Copy to copy the decimal number, or Download to save it (enter a custom file name when prompted).
🔢 Decimal → Binary
- Click the "Decimal → Binary" tab.
- Enter any non‑negative integer (or decimal fraction like
5.75). - The binary representation appears immediately, with the remainder‑division method shown in the formula area.
- Copy or download the result.
📊 Quick Reference Table
| Binary | Decimal | Binary | Decimal |
|---|---|---|---|
| 0 | 0 | 1000 | 8 |
| 1 | 1 | 1010 | 10 |
| 10 | 2 | 1111 | 15 |
| 11 | 3 | 10000 | 16 |
| 100 | 4 | 11111111 | 255 |
Real‑Time Conversion
Results update as you type — no need to click Convert.
Fractional Support
Handles binary fractions like 101.11 and decimal fractions like 5.75.
Step‑by‑Step Formula
See how the conversion is done, great for learning.
Quick Reference Cards
Click any card to load an example.
Custom Download Name
Prompt asks for a file name before saving.
100% Private
All processing happens locally in your browser.
❓ FAQ
Multiply each binary digit by 2 raised to its position (starting from 0 on the right) and sum all values. Example: 1101₂ = 1×8 + 1×4 + 0×2 + 1×1 = 13.
Repeatedly divide the decimal number by 2 and record the remainders. Read the remainders from bottom to top. Example: 13 → 1101.
Yes, both binary and decimal fractions are supported. For binary fractions, each digit after the point represents a negative power of 2.
There is no strict limit, but very large numbers may be displayed in scientific notation for readability.
100% free, part of All‑in‑One Utility Hub.