Binary number system is also known as base 2 number system which contain and manipulate only two digits either 0 or 1. As the name implies “bi” means two which start doing conversion from the left side. Now the question is why we are doing conversion and This Binary system exist, here is the solution as we know binary numbers are understand by computer only so we need to convert them in decimal or the other system which contain digit 0-9. Example of conversion, start from the left most digit and multiply it with 2^0 and next with 2^1 and each consecutive numbers with the increase in power such as: here is the binary string of 100101 convert it into decimal: 1×2^5 + 0×2^4 + 0×2^3+ 1×2^2 + 0×2^1 + 1×2^0 =32+0+0+8+1 = 41.
The Pingala who was the Indian Scholar developed a binary system. Binary numbers are found in Vedic literature and in the shastras which was written in Sanskrit and later committed to text by Pingala in 4th century. Now the mankind has progressed beyond Sanskrit. Now the Shastras found that mankind memory began to decline so they require texts and books to keep tracking all important information. Then binary code were traced to these text and after that in 17th century Gottfried Leibniz the father of calculus and great philosopher derived a system of logic which represent a verbal statement into mathematical code. His theory determine that simple codes and combination of zeros and ones could make life easy. But he does not known where to use this system. Then with the help of George Boole and his Boolean logic algebraic operations are used with the system of on/off of zeros and ones. Then on/off codes are implemented by computers with the unlimited numbers of application. Now All computer languages based on the logic of binary system.
The Common application of the binary number is provided by computer technology. As we discussed above, computer language and its programming is based on base-2 system which is used for digital encoding. Basically Digital encoding is the process of taking data and represent it into a discrete format and that format consist of groups of zeros and ones. Lets take an example the image you see on your computer screen have been encoded with a binary line in which each pixel contain a binary value. If a screen is using 16-bit code then there are 2^16 different colors and there combination to represent bits of zeros and ones. It is also in the mathematics field known as Boolean algebra which is concerned with logic and truth tables.
Advantage of using binary system is easily implemented in electronic systems using on or off signals. .They are either true or false and if we talk in terms of binary numbers 0 is considered as false and 1 is true. Provide low possibility of errors and reliable operation because when the data transfer it has to decide between on or off state and no disruption during the process will not disrupt the decision.