Q. Explain Hexadecimal Number System?

A Hexadecimal Number System:

uses base 16

includes only the digits 0 through 9 and the letters A, B, C, D, E, and F

In the Hexadecimal number system, the hex values are greater than 9 carry the following decimal value:

Above table provides all the information you'll ever need to convert from one number base into any other number base for the decimal values from 0 to 16.

To convert the hexadecimal number into a binary number, simply break the binary number into 4-bit groups beginning with the LSB and substitute the corresponding four bits in binary for each hexadecimal digit in the number.

For illustration, to convert 0ABCDh into a binary value, simply convert each hexadecimal digit according to the table above. The binary equivalent is:

To convert a binary number into the hexadecimal format is almost as easy. The first step is to filling the binary number with leading zeros to make sure that the binary number contains multiples of four bits. For illustration, given the binary number 10 1100 1010, the first step would be to add two bits in the Most Significant Bit (MSB) position so that it contains 12 bits. The revised binary value is 0010 1100 1010.

The next step is to divide the binary value into groups of four bits for example 0010 1100 1010. Lastly, look up these binary values in the table above and substitute the appropriate hexadecimal digits for example 2CA.

The weighted values for every position are as follows:

3DA = (3 x 16²) + (13 x 16¹) + (10 x 16⁰)

or

3DA = 768 + 208 + 10 =986