Use our Decimal to Binary Converter to instantly change decimal numbers (base 10) into binary (base 2). Perfect for students, programmers, and learners — includes examples, formulas, and step-by-step explanations.
Understanding the Decimal to Binary conversion is one of the most important concepts in mathematics and computer science. Every digital system, from simple calculators to modern supercomputers, runs on binary numbers — 0s and 1s.
Our Decimal to Binary Converter makes this process instant and accurate. You don’t need to do manual calculations or remember complex formulas. Just enter your decimal number and get the exact binary equivalent in seconds.
Decimal to Binary conversion means converting a number from base 10 (decimal) to base 2 (binary).
The decimal system uses digits from 0 to 9.
The binary system uses only 0 and 1.
For example:
Decimal 2 → Binary 10
Decimal 5 → Binary 101
Decimal 10 → Binary 1010
Computers understand only binary (0s and 1s). So when we input decimal numbers, the system internally converts them into binary to perform operations.
SEO Pheonix online Decimal to Binary Converter follows a simple algorithm:
It’s fast, accurate, and free to use — ideal for students, engineers, and programmers.
If you want to understand how it works, here’s the division-by-2 method, the most common manual technique.
Steps:
Divide the decimal number by 2.
Write down the remainder (0 or 1).
Divide the quotient by 2 again.
Continue dividing until the quotient becomes 0.
The binary number is the remainder sequence read from bottom to top.
| Step | Division | Quotient | Remainder |
| 1 | 13 ÷ 2 | 6 | 1 |
| 2 | 6 ÷ 2 | 3 | 0 |
| 3 | 3 ÷ 2 | 1 | 1 |
| 4 | 1 ÷ 2 | 0 | 1 |
Binary = 1101
✅ Decimal 13 = Binary 1101
| Decimal | Binary |
| 0 | 0 |
| 1 | 1 |
| 2 | 10 |
| 3 | 11 |
| 4 | 100 |
| 5 | 101 |
| 6 | 110 |
| 7 | 111 |
| 8 | 1000 |
| 9 | 1001 |
| 10 | 1010 |
| 11 | 1011 |
| 12 | 1100 |
| 13 | 1101 |
| 14 | 1110 |
| 15 | 1111 |
| 16 | 10000 |
| 17 | 10001 |
| 18 | 10010 |
| 19 | 10011 |
| 20 | 10100 |
The mathematical formula for converting decimal to binary is based on powers of 2:
N=bn×2n+bn-1×2n-1+...+b1×21+b0×2n
Where:
N = Decimal number
b = Binary digits (0 or 1)
Each binary digit represents an increasing power of 2 from right to left.
Binary is a base-2 system, meaning it uses only two symbols — 0 and 1. Each bit (binary digit) represents a power of 2.
Example:
Binary 1010 means
= 1×2³ + 0×2² + 1×2¹ + 0×2⁰
= 8 + 0 + 2 + 0
= 10 (decimal)
So binary 1010 = decimal 10.
Simplicity in computation – Only 0 and 1 are used.
Error detection – Easier to find and fix bit-level issues.
Hardware efficiency – Digital circuits operate in binary states (on/off).
Universal system – Used in all computing and networking devices.
Secure data processing – Binary allows encrypted bit-level operations.
Binary numbers are used everywhere — Even when we don’t notice!
Computers & Smartphones: Process data internally in binary form.
Digital Electronics: Signals represented as high (1) and low (0) voltage.
Programming languages: Binary operations in C, C++, Java, Python.
Networking: IP addresses and subnet masks use binary.
Machine learning & AI: Data encoding and model training rely on binary matrices.
✅ 100% Free and Instant Conversion
✅ Accurate results for large numbers
✅ Works for both integers and fractions
✅ No signup or installation required
✅ Mobile-friendly & easy interface
✅ Step-by-step guide for learning
SEO Pheonix Decimal to Binary Converter tool is perfect for students preparing for exams, programmers writing code, or anyone working on digital electronics.
You can also convert decimal fractions into binary using a slightly different method.
Steps:
Multiply the fractional part by 2.
Record the integer part (0 or 1).
Repeat with the new fractional part.
Stop when the fraction becomes 0 or reaches desired precision.
Example: Convert 0.625 to binary.
0.625 × 2 = 1.25 → integer = 1
0.25 × 2 = 0.5 → integer = 0
0.5 × 2 = 1.0 → integer = 1
Binary = 0.101
So, (0.625)₁₀ = (0.101)₂
SEO Pheonix Decimal to Binary Converter stands out because it combines speed, accuracy, and learning support.
🔹 No ads or clutter — clean interface.
🔹 Works on all browsers and mobile devices.
🔹 Ideal for students, programmers, and tech learners.
🔹 Includes real-time results and binary table.
🔹 Updated for 2025 with the latest web standards
The Decimal to Binary Converter is a fast, simple, and accurate way to transform decimal numbers into binary format. Whether you’re learning number systems, programming in C or Python, or designing digital circuits, this converter saves you time and effort.
No more manual calculations — just enter your number and get the binary output instantly.
Start using the Decimal to Binary Converter now and make number conversions effortless!
Binary is a number system that uses only two digits — 0 and 1 — to represent all values. Computers use this system for calculations and data storage.
Divide the decimal number by 2 repeatedly, note the remainders, and read them in reverse. Or simply use our Decimal to Binary Converter for instant results.
255 in binary is 11111111.
Because electronic devices have two states — ON (1) and OFF (0), which perfectly match the binary system.