Hex Calculator

Hexadecimal Calculator

Hexadecimal is a positional number system with base 16. Unlike the decimal system, which uses ten digits from 0 through 9, hexadecimal uses sixteen symbols: 0 through 9 and the letters A through F.

The letters A, B, C, D, E, and F represent the decimal values 10, 11, 12, 13, 14, and 15 respectively. Therefore, the hexadecimal number FF represents 15 × 16 + 15, which equals 255 in decimal.

Hexadecimal Number System

Each position in a hexadecimal number represents a power of 16. Starting from the rightmost position, the place values are 16°, 16¹, 16², 16³, and so on.

Hexadecimal to Decimal

To convert a hexadecimal number to decimal, multiply each digit by the corresponding power of 16 and add the resulting values.

For example, the hexadecimal value FF can be converted as follows:

Hexadecimal to Binary

Hexadecimal has a particularly useful relationship with binary. Every hexadecimal digit corresponds exactly to four binary bits. This makes it possible to convert between hexadecimal and binary directly without performing a decimal conversion first.

For example, FF₁₆ becomes 1111 1111₂ because each F represents the four-bit binary sequence 1111.

Hexadecimal to Octal

Octal is a base-8 number system that uses the digits 0 through 7. Hexadecimal and octal do not have the same direct digit-to-bit relationship, so a convenient conversion method is to convert the hexadecimal value to decimal and then convert the decimal value to octal.

For example:

Why Hexadecimal Is Used in Computing

Hexadecimal is widely used in computer science because it provides a compact way to represent binary information. Since one hexadecimal digit represents four binary bits, long binary sequences can be written using far fewer characters.

Hexadecimal values are commonly encountered in programming, memory addresses, machine-level data, debugging, bitwise operations, and other areas involving digital information.

Hexadecimal and Binary Bits

The relationship between hexadecimal and binary makes it easy to determine the binary representation of a hexadecimal number. A hexadecimal value containing four digits represents up to sixteen binary bits, while eight hexadecimal digits represent up to thirty-two bits.

Valid Hexadecimal Characters

A hexadecimal number can contain only the digits 0 through 9 and the letters A through F. Lowercase letters a through f are also valid and represent the same values as their uppercase forms.

How to Use the Hexadecimal Calculator

Enter a hexadecimal number using digits 0–9 and letters A–F. Then select whether you want to convert it to decimal, binary, or octal. The calculator validates the input and displays the selected conversion together with the other equivalent number representations.

The result also provides the conversion steps, binary representation, bit information, and an explanation of what the resulting value means.