# Number Systems Concepts

The study of number systems is useful to the student of computing due to the fact that many number systems other than the familiar decimal (base 10) number system, is used in the computer field.

Digital computers internally use the binary (base 2) number system to represent data and perform arithmetic calculations. The binary number system is very efficient for computers, but not for humans. Representing even relatively small numbers with the binary system requires working with long strings of ones and zeroes.

The hexadecimal (base 16) number system (often called “hex” for short) provides us with a shorthand method of working with binary numbers. Less commonly used is the octal (base 8) number system, where one digit in octal corresponds to three binary digits (bits).

The decimal number system that we are familiar with is a positional number system. The actual number of symbols used in a positional number system depends on its ha_s_e_(also called the @(1i35). The decimal number system has a base of 10, so the numeral with the highest value is 9; the octal number system has a base of 8, so the numeral with the highest value is 7; the binary number system has a base of 2, so the numeral with the highest value is 1, etc.

Any number can be represented by arranging symbols in specific positions. You know that in the decimal number system, the successive positions to the left of the decimal point represent units (ones), tens, ‘ hundreds, thousands, etc. Put another way, each position represents the power of base 10. For example, the decimal number 1,275 (written 1,275„‚).

### Converting a Decimal Number to a Binary Number

To convert a decimal number to its binary equivalent, the remainder method can be used. (This method can be used to convert a decimal number into any other base.) The remainder method involves the following four steps:

- Divide the decimal number by the base (in the case of binary, divide by 2).
- Indicate the remainder to the right.
- Continue dividing into each quotient (and indicating the remainder) until the divide operation produces a zero quotient
- The base 2 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).

(The base 2 number is the numeric remainder reading from the last division to the Erst (if you start at the bottom, the answer will read from top to bottom).