# Hexadecimal Number system

The hexadecimal (base 16) number system is a positional number system as are the decimal number system and the binary number system. Recall that in any positional number system, regardless of the base, the highest numerica1 symbol always has a value of one less than the base. Furthermore, one and only one symbol must ever be used to represent a value in any position of the number.

For number systems with a base of 10 or less, a combination of Arabic numerals can be used to represent any value in that number system. The decimal number system uses the Arabic numerals 0 through 9; the binary number system uses the Arabic numerals 0 and 1; the octal number system uses the Arabic numerals 0 through 7, and any other number system with a base less than 10 would use the Arabic numerals from 0 to one less than the base of that number system.

However, if the base of the number system is greater than 10, more than 10 symbols are needed to represent all of the possible positiona1 values in that number system. The hexadecimal number system uses not only the Arabic numerals 0 through 9, but also uses the letters A, B, C, D, E, and F to represent the equivalent of 1010 through 1510, respectively.

### Converting a Decimal Number to a Hexadecimal N umber

To convert a decimal number to its hexadecimal equivalent, the remainder method (the same method used in converting a decimal number to its binary equivalent) can be used. To review, the remainder method involves the following four steps:

- Divide the decimal number by the base (in the case of hexadecimal, divide by 16).
- Indicate the remainder to the right. If the remainder is between 10 and 15, indicate the corresponding hex digit A through F.
- Continue dividing into each quotient (and indicating the remainder) until the divide operation produces a zero quotient.
- The base 16 number is the numeric remainder reading from the last division to the first (if you start at the bottom, the answer will read from top to bottom).