In digital electronics representation, there is various number system are used. The most common number systems used are decimal, binary, octal and hexadecimal systems.
Decimal Number System
The number system that we use in our day to day life is called decimal number system. The decimal number is a positional number system (The value of a digit depends on its position) that uses 10 as a base to represent different values. This number system is composed of 10 numeral symbols (Deca means 10 and so it is called decimal systems).
The 10 symbols in decimal system are 0,1,2,3,4,5,6,7,8, and 9.
For example, consider the decimal number 1234.456, here the value 1234, which comes before the decimal point , is called integer value and the value 456, which comes after the decimal point, is called fraction value.
1×103+2×102+3×101+4×100+4×10-1+5×10-2+6×10-3 = 1000+200+30+4+0.4+0.05+0.006 = 1234.456
Binary Number System
It is very difficult to design electronic equipment which works with 10 different voltage levels (decimal digits 0 to 9). To overcome this difficulty the base 2 number system is used which is called Binary Number System.
In binary, there are only two symbols or digits 0 and 1. The binary system is also a positional value system, where each binary digit has its own value or weight expressed as powers of 2. For example, consider the binary number 1010.101.
The value of this binary number can be obtained as:
1×23 + 0×22 + 1×21 + 0×20 + 1×2-1 + 0×2-2 + 1×2-3 = 8 + 2 + 0.5 + 0 + 0.125 = 10.625
Octal Number System
The octal number system is very important in digital computer. The octal number system is a positional number system which represents base 8. This number system has 8 digits or symbols which are 0,1,2,3,4,5,6 and 7.
The octal number system is expressed as the power of 8. For example, consider the octal number 215.43. The value of this octal number can be obtained as:
2×82 + 2×81 + 5×80 + 4×8-1 + 3×8-2 =128 + 8 + 5 + 0.5 + 0.0469 = 141.5469
Hexa Decimal Number System
The hexadecimal number system is a base 16 number system. Thus it has 16 possible digit symbols. It uses A for 10, B for 11, C for 12, D for 13, E for 14 and F for 15. Thus the Hexadecimal number system has 16 unique symbols which are given below:
0 to 9 (0,1,2,3,4,5,6,7,8,9) and A to F (A,B,C,D,E,F).
Like any other number system, Hexadecimal is also a positional value system, where each hexadecimal value has its own value or weight expressed as a power of 16.
For example, consider the hexadecimal number (4A9.2B)16.
In the hexadecimal system, the point used to separate the integer and the fraction part of a number is known as the hexadecimal point. The value of the hexadecimal number can also be determined as the sum of the products of the symbol multiplied by the weight of the symbol itself. Therefore the value of the given hexadecimal number is:
=4×162 + 10×161 + 9×160 + 2×16-1 + 11×16-2 = 1024 + 16 + 9 + 0.125 + 0.042 = 1193.1679.
The hexadecimal number (4A9.2B)16. represents the decimal number (1193.1679)10.