Base 16 to Decimal Calculator

Enter hexadecimal numbers and get decimal answers. Review powers, fractions, signed values, and export options. Use examples to verify each conversion step today quickly.

Calculator

Use 0-9 and A-F. Fractions are allowed.
Choose decimal places for fractional hex values.
Used only when signed mode is checked.

Formula Used

Decimal value is the sum of each hexadecimal digit multiplied by a power of 16.

Formula: decimal = dn × 16n + ... + d0 × 160.

Example Data Table

Base 16 Input Place Value Work Decimal Output
1A 1 × 16 + 10 26
FF 15 × 16 + 15 255
7B 7 × 16 + 11 123
A3.F 10 × 16 + 3 + 15/16 163.9375
0x100 1 × 16² 256

How to Use This Calculator

Enter a hexadecimal value in the input box. You may include a leading 0x, a sign, or a fractional point. Select precision when the number has fractional digits. Choose a grouping style for the output. Enable signed mode only for whole numbers stored in fixed-width two's complement form. Press Calculate to see the result above the form. Use CSV or PDF buttons to save the same result.

Understanding Base 16 to Decimal Conversion

Base 16 is also called hexadecimal. It uses sixteen symbols. The first ten symbols are 0 through 9. The next six symbols are A through F. A means 10. B means 11. C means 12. D means 13. E means 14. F means 15.

Why Base 16 Matters

Hexadecimal values appear in programming, networking, color codes, memory addresses, and digital electronics. A compact hex value can represent long binary data. One hex digit equals four binary bits. That makes it useful when reading machine-level values.

How Place Values Work

Decimal numbers use powers of ten. Hexadecimal numbers use powers of sixteen. The rightmost whole digit uses 16 raised to zero. The next digit uses 16 raised to one. Each step left increases the power by one.

For example, A3 equals 10 multiplied by 16 plus 3. The answer is 163. A fractional digit works in the opposite direction. The first digit after the point uses 16 raised to negative one. The second uses 16 raised to negative two.

Advanced Input Options

This calculator accepts lowercase and uppercase letters. It can also clean spaces, commas, and underscores. That helps with copied values from code, logs, or tables. Fraction precision controls how many decimal digits appear after conversion.

Signed Hex Values

Some systems store negative numbers with two's complement rules. In that case, the same hex value can mean a positive or negative decimal number. The selected bit width decides the signed interpretation. FF is 255 as unsigned. In 8-bit signed form, FF becomes -1.

Common Conversion Mistakes

Many errors come from treating A through F like normal letters. Another mistake is using powers of ten instead of powers of sixteen. Fractional values can also be misread when precision is too low. Use the displayed formula to compare every digit with its correct position before trusting the output.

Useful Result Checks

The expansion line shows each digit and power. It helps students and developers audit the answer. The export buttons make it easier to save homework, reports, or test cases. Always choose the correct signed mode before using the final value.

FAQs

What is a base 16 number?

Base 16 is a number system with sixteen symbols. It uses 0 to 9 and A to F. The letters represent decimal values from 10 to 15.

How do I convert base 16 to decimal?

Multiply each hexadecimal digit by its matching power of 16. Add all products together. For fractions, use negative powers of 16 after the point.

Can this calculator convert fractional hex values?

Yes. Enter a value such as A3.F or 0x1.C. The calculator converts the whole part and fractional part, then combines them.

What does A mean in hexadecimal?

A means 10 in decimal. B means 11, C means 12, D means 13, E means 14, and F means 15.

Why does signed mode change the answer?

Signed mode treats the value as two's complement data. The highest bit can mark a negative number, depending on the selected bit width.

Can I enter 0x before the number?

Yes. The calculator accepts a leading 0x prefix. It removes the prefix before validating and converting the hexadecimal value.

Does letter case matter?

No. Lowercase and uppercase hex letters work the same. The calculator normalizes letters before performing the decimal conversion.

What can I export from the calculator?

You can download the result as CSV or PDF. Both exports include the input, cleaned value, decimal answer, and formula expansion.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.