Free Computer Science Tool
Binary to Decimal Converter
Convert binary numbers into decimal numbers instantly. Enter any binary value using only 0 and 1, then see the decimal answer with a simple step-by-step explanation.
13
Useful for computer science students, programming beginners, digital systems learners, and number system practice.
Quick examples:
Decimal Result
13
Binary 1101 equals decimal 13.
Binary Digits
4 bits
Place Values Used
2³ to 2⁰
Simple Explanation
Method
Place value method
Status
Valid binary
| Binary Digit | Position | Power of 2 | Decimal Value |
|---|---|---|---|
| 1 | 3 | 2³ = 8 | 1 × 8 = 8 |
| 1 | 2 | 2² = 4 | 1 × 4 = 4 |
| 0 | 1 | 2¹ = 2 | 0 × 2 = 0 |
| 1 | 0 | 2⁰ = 1 | 1 × 1 = 1 |
| Concept | Example | Simple Meaning |
|---|---|---|
| Binary Number | 1101₂ | A number written in base 2 using only 0 and 1. |
| Decimal Number | 13₁₀ | A normal base-10 number used in daily life. |
| Rightmost Digit | 2⁰ | The rightmost binary digit starts from power 0. |
| Conversion Rule | Digit × 2ᵖᵒˢⁱᵗⁱᵒⁿ | Multiply each binary digit by its power of 2 and add the values. |
Binary Uses 0 and 1
Binary numbers are made with only two digits, which makes them important in computers and digital systems.
Each Position Matters
Every digit has a position value. From right to left, the powers are 2⁰, 2¹, 2², 2³, and so on.
Add the Values
Only the positions with digit 1 add value. Positions with digit 0 add nothing to the decimal result.
Note: This converter accepts only binary digits 0 and 1. Spaces are automatically removed, so values like “1010 1100” can still be converted.
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