🎓 Mathematics • Mathematical Conversions
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Binary Converter
Converts base-2 binary to decimal, hexadecimal, octal, and ASCII text with bit length counting.
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 Binary?
Binary is the base-2 numeral system using only digits 0 and 1, the fundamental language of digital computers.
Formula & Step-by-Step Calculation
N = ∑ dᵢ × 2ⁱ
Sum of bit values multiplied by positional powers of 2.
Worked Step-by-Step Examples
Example 1
Convert 1010₂
Solution: 10 in decimal
• 1(8) + 0(4) + 1(2) + 0(1) = 8 + 2 = 10
Common Real-World & Academic Use Cases
- ✓ Computer architecture programming
- ✓ IP address subnet masking
- ✓ Digital electronics logic
How to Use the Binary Converter
1
Enter Binary
Type 0s and 1s.
2
Inspect Bases
View decimal, hex, and octal equivalents.
Frequently Asked Questions
Q: What is a byte?
A group of 8 binary digits (bits).