Hexadecimal Calculator

About Hexadecimal Calculator

Hexadecimal (base 16) uses digits 0-9 and letters A-F. Common in computing for representing colors, memory addresses, etc.

How to use this calculator

1. Enter the number you want to convert.
2. Choose whether it is hexadecimal or decimal.
3. Read the converted value in the other number system.
4. Use the worked example to check how the place values change.

The formula explained

The notation \(n_{16} \leftrightarrow n_{10}\) means a number can be converted between base 16 and base 10. In hex, each position represents a power of 16, while in decimal each position represents a power of 10.

• \(n_{16}\) = a number written in hexadecimal, using digits 0 to 9 and letters A to F
• \(n_{10}\) = the same number written in decimal

Step by step method

1. For hex to decimal, expand the number by place value, so for 3A you compute \(3 \times 16^1 + 10 \times 16^0\).
2. For decimal to hex, divide by 16 repeatedly and record the remainders.
3. Write the remainders from last to first to get the hexadecimal form.

Worked example

Problem. Convert hexadecimal 3A to decimal.

1. Split 3A into place values, \(3\) and \(A\), where \(A = 10\).
2. Compute \(3 \times 16 + 10 \times 1 = 48 + 10\).
3. Add them to get \(58\).

Tips and common mistakes

• Remember that A, B, C, D, E, and F stand for 10, 11, 12, 13, 14, and 15.
• A common mistake is treating hex digits like decimal digits, but each position in hex is based on powers of 16.

Frequently asked questions