Computers operate by means of the binary number system using only two digits 0 and 1. How does the system work?

Electronic digital computers handle numbers in the binary form, which means that the ordinary or decimal numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 are written in binary notation as follows: 0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010. It is easy to deduce the rules from this. In essence, binary system works in the same way as decimal in that once all the symbols have been used in one column, another column is added to the left. In binary system:

 Zero = 0 

One = 1 

Having used the two binary numbers for zero and one respectively, we have to add a column to the left just as we do after using the last digit 9 in the decimal system. Thus, in binary number system: 

Two = 10 

Three = 11

Again another column is added, followed by yet another column to represent subsequent numbers shown below: 

One = 1 

Four = 100 

Five = 101 

Six = 110 

Seven = 111 

Eight = 1000 

Nine = 1001 

Ten = 1010... \and so on. 

Whereas in the decimal system each column represents additional power of ten, in binary each column represents an additional power of two. The point is you 'carry 1, i.e. move the digit 1 a place to the left, when you reach 2. In decimal notation, you move 1 a place left when you reach 10. In other words, instead of columns for units, tens, hundreds, thousand etc. the columns are for units, twos, fours, eights etc. So, in binary notation: '1 +1 = 0 with 1 to carry'. The advantage of the binary system for use in digital computers is that only two electronic states, off and on, are required to represent all binary digits, which in turn represent specific decimal numbers.