q explain hexadecimal number systema hexadecimal

Question

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:

Binary	Octal	Decimal	Hex
0000B	00Q	00	00H
0001B	01Q	01	01H
0010B	02Q	02	02H
0011B	03Q	03	03H
0100B	04Q	04	04H
0101B	05Q	05	05H
0110B	06Q	06	06H
0111B	07Q	07	07H
1000B	10Q	08	08H
1001B	11Q	09	09H
1010B	12Q	10	0AH
1011B	13Q	11	0BH
1100B	14Q	12	0CH
1101B	15Q	13	0DH
1110B	16Q	14	0EH
1111B	17Q	15	0FH
1 0000B	20Q	16	10H

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:

0ABCDH

=

0000 1010 1011 1100 1101

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:

16^3	16^2	16^1	16^0
4096	256	16	1

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

or

3DA = 768 + 208 + 10 =986