🎓 Mathematics • Mathematical Conversions
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Decimal Converter
Converts base-10 decimal integers into binary, hexadecimal, octal, BCD, and Roman numerals.
Radix & Positional Engine
Number Base Conversion Studio
Perform positional conversions between Binary, Decimal, Hexadecimal, Octal, and arbitrary Base-N with step-by-step division tables and visual 4-bit nibbles.
Direction
Decimal Result
11010110₂ =
214₁₀
Sum: 2^7 (128) + 2^6 (64) + 2^4 (16) + 2^2 (4) + 2^1 (2) = 214
Positional Powers of 2 Breakdown
| Power | Weight (2^n) | Bit | Calculation | Contribution |
|---|---|---|---|---|
| 2^7 | 128 | 1 | 1 × 128 | 128 |
| 2^6 | 64 | 1 | 1 × 64 | 64 |
| 2^5 | 32 | 0 | 0 × 32 | 0 |
| 2^4 | 16 | 1 | 1 × 16 | 16 |
| 2^3 | 8 | 0 | 0 × 8 | 0 |
| 2^2 | 4 | 1 | 1 × 4 | 4 |
| 2^1 | 2 | 1 | 1 × 2 | 2 |
| 2^0 | 1 | 0 | 0 × 1 | 0 |
What is Decimal Base-10?
The decimal system uses ten symbols (0–9) and positional powers of 10, the universal standard for human calculation.
Formula & Step-by-Step Calculation
Repeated division by target base (2, 8, or 16)
Remainders read in reverse order generate the target base representation.
Worked Step-by-Step Examples
Example 1
Convert 255 to hex
Solution: FF
• 255 / 16 = 15 remainder 15 (F), 15 / 16 = 0 remainder 15 (F) ⟹ FF
Common Real-World & Academic Use Cases
- ✓ Software development memory addressing
- ✓ Networking
- ✓ Digital electronics
How to Use the Decimal Converter
1
Enter Decimal
Type integer.
2
View Target Bases
Read binary, hex, and octal.
Frequently Asked Questions
Q: What is BCD?
Binary Coded Decimal encodes each decimal digit into a 4-bit nibble.