Calculator
Accepted formats: 101.101, 0.011, .101, -110.01.
Example Data Table
| Binary Fraction | Expanded Form | Decimal Result |
|---|---|---|
| 0.1 | 1 × 2-1 | 0.5 |
| 1.01 | 1 × 20 + 1 × 2-2 | 1.25 |
| 10.11 | 1 × 21 + 1 × 2-1 + 1 × 2-2 | 2.75 |
| 101.101 | 1 × 22 + 1 × 20 + 1 × 2-1 + 1 × 2-3 | 5.625 |
| 1111.0001 | 1 × 23 + 1 × 22 + 1 × 21 + 1 × 20 + 1 × 2-4 | 15.0625 |
Formula Used
A binary fraction converts to decimal by summing each bit times its power of two. Bits left of the point use nonnegative exponents. Bits right of the point use negative exponents.
Decimal Value = Σ(bi × 2i) + Σ(fj × 2-j)
Example: 101.1012 = 1×22 + 0×21 + 1×20 + 1×2-1 + 0×2-2 + 1×2-3
That becomes 4 + 0 + 1 + 0.5 + 0 + 0.125 = 5.625.
How to Use This Calculator
- Enter a binary fraction in the input field.
- Use one decimal point if the number has fractional bits.
- Set your preferred decimal display precision.
- Choose whether trailing zeros should be trimmed.
- Press Convert Now to view the result.
- Read the exact value, rounded value, and place-value table.
- Review the Plotly graph for visual contribution analysis.
- Download the results as CSV or PDF if needed.
FAQs
1) Can this calculator handle leading zeros?
Yes. Leading zeros do not change the decimal value. They still appear in the place-value process, which helps when teaching fixed-width binary formats or reviewing bit positions.
2) Can I enter negative binary fractions?
Yes. Start the input with a minus sign, such as -110.01. The calculator converts the magnitude first, then applies the negative sign to the final decimal result.
3) Why do binary fractions end in finite decimals?
Binary fraction denominators are powers of two. Decimal fractions terminate whenever the denominator contains only factors of two and five after simplification, so binary fractions always terminate in decimal form.
4) What if my value has no fractional part?
You can enter a whole binary number like 1011. The calculator still works and returns the decimal integer result without needing fractional digits.
5) Does rounding change the exact answer?
No. The exact decimal result remains available separately. Rounding only changes the display output according to the precision setting you choose for viewing or exporting.
6) How are place values assigned?
Bits left of the binary point use 20, 21, 22, and higher. Bits right of the point use 2-1, 2-2, 2-3, and so on.
7) What do the CSV and PDF exports include?
Both exports include the input value, exact result, rounded result, settings, and the full step table. This makes the page useful for documentation, classroom work, and audit notes.
8) Is this calculator useful for students?
Yes. It shows the formula, a worked example, the full contribution table, and a graph. That combination supports both quick answers and concept-based learning.