Introduction to Number Systems 

The term number system used in digital circuits. A digital circuit operates with binary numbers, i.e. only in two states. The output of the circuit is either low (0) or high (1) in a positive logic system. Every computer stores numbers, letters, and other special characters in a coded form. So for this reason, it is essential to know about the number system. So the goal of this chapter is to familiarize you with the basic fundaments of number system. It also introduces some of the commonly used number systems by computer professionals and the relationship between them.

Number System 

The decimal number system which is commonly having digits 0,1,2,3..........9 and combination of each digit and the number system that we use in day to day life is called decimal number system. In this system, the base is equal to 10. So many other number systems used in the computer system and also in the digital electronics. There are many other number systems like binary, octal, hexadecimal, etc. It is also possible to convert the one number system into another number system. It is possible to express a number in any base or radix "X". In the binary number system, the base (radix) is 2. In the octal number system, the base is 8 and in the hexadecimal number system, the base is 16.

Binary Number System 

The binary number system is simple because it consists of only two digits, i.e. 0 and 1. Just as the decimal system with its tem digits is a base-ten system, the binary system with its two digits is a base-two system. The position of 0 or 1 in binary number indicates its "weight" within the number. In a binary number, the weight of each successively higher position to the left is an increasing power of two.

For example, in the decimal number system,

(198)₁₀=1x10²+ 9x10¹+ 8x10⁰

                                                         Hundreds   tens    units

Similarly, binary numbers are also represented by positional weights.

For example,

                   (198)₁₀  = (11000110)₂

                                  = 1x2⁷+1x2⁶+0x2⁵+0x2⁴+0x2³+1x2¹+0x2⁰

                                  = 128+64+0+0+0+4+2+0 = 198

In the digital system, each of the binary digits is called a bit and a group of 4 and 8 bits are called a nibble and a byte respectively. The highest decimal number that can be represented by n-bits binary number is 2ⁿ-1 (beginning with zero). Thus with an 8-bit binary number, the maximum decimal number that can be represented is 2⁸-1=255.