Binary Coding System
We normally use a decimal number system in our day to day life. It has the digits 0, 1, 2,….. .8, 9 as symbols for representing numbers. It is a positional number system with representing data. It has only two symbols 0 and 1 (ON and OFF of a switch) called bits or binary digits. In computers, therefore, numbers are represented using these two digits only and this system of representation of data is called as binary coding system.
Even though computer has only two symbols 0 and 1, it can represented all the numeric quantities, alphanumeric characteristics (numbering around 60), by using a set of these bits. For example, a set of 3 such bits can represent 8 different characters because it is possible to form 8 different combinations from 8 bits of more. Even if uses 8 bits of more. Even if it uses 8 bit word, it can have 28 =256 such combinations and hence it can very easily represent all these alphanumeric characters.2
In computers, each alphanumeric character is coded in the form of a separate set of bits. This code is termed as Binary Code, Arithmetic operations in computer use numbers coded in Binary from. Binary number system is also a positional number system with two symbols 0 and 1 with appropriate positional values. The positional values are found by raising the base of the number system to the power of the position.
Any combination of 0s and as a valid binary number. It can be converted to its decimal equivalent by multiplying each digit with its positional value as illustrated below:
(1101)2 = 1X2^3 + 1 X 2^2 X 0 X 2^1 + 1X2^0 = (13)10
Similarly a decimal integer can be converted in to its binary equivalent y repeated division by 2, as illustrated below:
Example: Conversion of 25 to binary form
|Number to be Divided by 2|
Collecting the reminders and starting binary number with last digit, we find that
(25)10 = (11001)2