Explain hexadecimal number system, Electrical Engineering

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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


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