Modern digital
technology is dependent entirely upon the binary number system, which has only
two elements, viz., 0 and 1, in it. However, we are more familiar with decimal
number system, which has ten basic elements (0 to 9) in it. In this chapter, we
discuss the principles of various number systems that we commonly come across
in various contexts. The discussion begins with the decimal number system. This
is followed by the binary, octal, and hexadecimal number systems.

**THE DECIMAL NUMBER SYSTEM**

The
decimal number system is the most commonly and widely used number system by the
common man. As stated above, we have ten elemental numbers in this number system.
They are, respectively, 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Since there are ten
digits in this group, we say that the number system has a

*base*or*radix*of 10*.*In the decimal number system, numbers greater than 9 are represented by repeatedly using these digits in a definite order. As an example, consider let us consider the decimal number 123. This may be expressed in the form (123)_{10},_{ }where the subscript 10*represents the base or radix of number 123. It can be seen that 123 represents a short form of expressing numbers. This may be expanded as:*
(123)

_{10}= (1 ´ 10^{2}) + (2 ´ 10^{1}) + (3 ´ 10^{0})
where digits 1, 2, and 3 are the
coefficients of the appropriate powers of ten (i.e., 10

^{2}, 10^{1}, and 10^{0}, respectively). Larger numbers can be expressed in similar fashion by writing them as coefficients of the powers of ten. In fact,*in any number system*,*numbers are expressed as coefficients of appropriate powers of the radix of the system.*
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