Decimal to Hex

Converting decimal to hexadecimal means changing a number from the base 10 numeral system to the base 16 numeral system. The decimal number system uses ten digits (0–9). The hexadecimal number system adds six more symbols — the hex digits A–F — to represent values 10 through 15.

Programmers and engineers prefer hexadecimal because it maps cleanly to binary numbers. Each hex digit represents exactly four binary bits. A single byte (8 bits) fits in just two hex digits. Memory addresses, color codes, and machine instructions become much easier to read than raw binary.

The standard method is the repeated division and remainder algorithm. Take the integer, divide it by 16, and record the remainder. That remainder maps to a hex digit. Then take the quotient and repeat until it reaches zero. Read the remainders from bottom to top — that's your hexadecimal result.

For example, converting the integer 255: divide 255 by 16 to get quotient 15 and remainder 15. Since 15 maps to F, the hex result is FF. Two divisions, two hex digits.

The decimal to hexadecimal formula uses repeated division by the radix (16). At each step, the remainder becomes one hex digit, and the quotient carries forward to the next step.