Free Computer Science Tool
Decimal to Binary Converter
Convert decimal numbers into binary numbers instantly. Enter any whole decimal number, then see the binary answer with a simple step-by-step repeated division explanation.
1101
Useful for computer science students, programming beginners, digital electronics learners, and number system practice.
Quick examples:
Binary Result
1101
Decimal 13 equals binary 1101.
Binary Length
4 bits
Method
Repeated division by 2
Simple Explanation
Status
Valid decimal
Input Type
Whole number
| Step | Division | Quotient | Remainder |
|---|---|---|---|
| 1 | 13 ÷ 2 | 6 | 1 |
| 2 | 6 ÷ 2 | 3 | 0 |
| 3 | 3 ÷ 2 | 1 | 1 |
| 4 | 1 ÷ 2 | 0 | 1 |
| Concept | Example | Simple Meaning |
|---|---|---|
| Decimal Number | 13₁₀ | A normal base-10 number used in daily life. |
| Binary Number | 1101₂ | A base-2 number used in computers and digital systems. |
| Remainder | 0 or 1 | Each division by 2 gives a remainder that becomes part of the binary answer. |
| Reading Rule | Bottom to top | After repeated division, read the remainders from the last step back to the first step. |
Decimal Is Base 10
Decimal numbers use ten digits from 0 to 9 and are the normal numbers we use every day.
Binary Is Base 2
Binary numbers use only 0 and 1, which makes them important in computers and digital electronics.
Divide by 2
To convert decimal to binary, divide by 2 repeatedly and collect the remainders.
Note: This converter accepts only non-negative whole decimal numbers. Commas, spaces, and underscores are automatically removed, so values like “1,024” and “1 024” can still be converted.
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