# Decimal Number System

**THE DECIMAL NUMBER SYSTEM**

The number systems are based on an ordered set of number of digits. The total number of digits used in a number system is called ‘base’ or ‘radix’ of the number system. The decimal number system used 10 digits - 0, 1, 2, ….. 9 and hence its base is 10. The base of binary number system is 2, base of octal number system is 8 and hexadecimal system has base 16. The decimal number system is the most popular system used not only by scientists and engineers but also by the common man. It is a positional number system as the value of any number depends on the position of digits.

e.g. Consider number 638.

Its representation is 638 = 600 30 8

i.e. 2 1 0

638_{10} = 6x10 ^{2} 3x10 ^{1} 8x10^{0}

Starting from left most digit, 6 is in the hundreds position. It is called t he Most Significant Digit (MSD). 3is in the tens position. The last digit 8 is in the unit position and is the least significant digit (LSD).

The example shows that the value of each position is a power of base 10. The power can be either positive, negative or 0.