Binary system

The word "binary" describes a system which has only 2 possible digits. Number system which uses only 2 values (0, 1; on, off) to represent codes and data. As zeros and ones can be easily represented by 2 voltages, the binary system is the foundation on which digital technology is built. Every digital computer whether a pocket calculator or a mainframe uses same binary notation.

 To understand this, let's 1st compare this to a system you are probably more familiar with, the Decimal system. Unlike decimal system, only 2 digits - 0, 1 - suffice to represent a number in binary system.  The binary system is vital in technology. The reason is that any electronic circuit can have 2 possible states, on or off. A simple example is light in your room. The switch has 2 options only, on or off. The binary system plays a crucial role in the computer science and technology.  The 1st 20 numbers in the binary notation are 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111, 10000, 10001, 10010, 10011, 10100, the origin of which can be better understood if they are re-written as follows:

1:    00001                        11:    01011
2:    00010                        12:    01100
3:    00011                        13:    01101
4:    00100                        14:    01110
5:    00101                        15:    01111
6:    00110                        16:    10000
7:    00111                        17:    10001
8:    01000                        18:    10010
9:    01001                        19:    10011
10:  01010                         20:   10100  

Any decimal number can be converted into binary system by summing the suitable multiples of different powers of 2. For instance, starting from the right, 10101101 represents (1 x 2⁰) + (0 x 2¹) + (1 x 2²) + (1 x 2³) + (0 x 2⁴) + (1 x 2⁵) + (0 x 2⁶) + (1 x 2⁷) = 173. This example can be used for conversion of the binary numbers into the decimal numbers. 

For conversion of the decimal numbers to binary numbers, same principle can be used, but the other way around. Therefore, to convert, 1st find the highest power of 2 which does not exceed the given number, and place a 1 in corresponding position in binary number.

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