Intenr of binary number system

It consists of only two numbers and hence this number system is also called base 2 or radix 2  number system.

                  As in the decimal number system, let us take us example of binary numbermatically as thes, which represents    more data than 0 and  1.   Let the binary number is 1101 and then as per the bit positions, each of the bit has a different weight. As shown in the case of decimal number system (base 10), the difference in weight will be in the multiple of base that is 2 in binary number system. So e can represent 1101 mathematically as below

                             Now you saw that when we use combination of 4 bits as above, we attained decimal 13. This means that if we want to represent 13, we should have at least four bits.

       Since, our basic objective is to represent decimal  number by binary digits, we have to find out how many bits are required to be combined in order to represent all digits of the decimal number system.

Let us start with 2 bits

Then the highest value would be

If the number system consists of 4-bit combination then it is termed as Hexadecimal Number   Symtem.  It is base 16 number system and hence consist of 16 numbers. Hexadecimal number is characterized by values between 0-15.But,since the digits after 9 are combined ,for example in 15,we have two decimal digits-1and 5.