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Hexadecimal number system

 

The hexadecimal number system represents numbers with a base of 16, meaning there are 16 possible values or symbols. The 16 values or symbols are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. The symbols from A to F represent numbers 10 to 15, respectively. To represent any value in hex, it requires 4 bits. They are either suffixed with x or h.

Representation of hexadecimal number system
 

Hex digit

0

1

2

3

4

5

6

7

Binary

0000

0001

0010

0011

0100

0101

0110

0111

decimal

0

1

2

3

4

5

6

7

 

Hex digit

8

9

A

B

C

D

E

F

Binary

1000

1001

1010

1011

1100

1101

1110

1111

decimal

8

9

10

11

12

13

14

15


 

Place value

Just like the decimal system, the hexadecimal system also has place values. Decimal has the powers of 10, while hexadecimal has the powers of 16.

Exponent

163

162

161

160

value

4096

256

16

1

 

Exponent

16-1

16-2

16-3

value

1/16

1/256

1/4096

 

hexadecimal

Decimal

10

16

100

256

1000

4096

 

Example 1 – The number 200 in the hexadecimal number system will be read as what in decimal?

-: = 2x162 + 0x161 + 0x160

   = 512

(200)16 = (512)10

 

Example 2 – The number 200 in the hexadecimal number system will be read as what in binary?

-:  2 – 0010        0 – 0000        0 – 0000

  (200)16 = (001000000000)2

  (200)16 = (1000000000)2

 

Applications of the hexadecimal number system

Sometimes, the binary number system uses hexadecimal in its place. Since 16 is equal to 24, they have a linear relationship between them. It means that one hex can store four binary digits. It shortens the code for the computer, making it easier to understand. It has undoubtedly more uses:

  • They are used to define locations in the memory.
  • Every color we see on a web page has a hex-code formed by two hexadecimal values. The format of any color is #RRGGBB, where RR signifies red, GG is green, and BB is blue.
  • They are also used to refer to MAC (Media Access Control) addresses. They are 12-digit hexadecimal values. Their format is either MM:MM:MM:SS:SS:SS or MMM-MMSS-SSSS. The first six digits of the address represent the adapter's manufacturer's ID, while the last six digits represent the adapter's serial number.
  • They also define the memory location of the errors and are helpful to the programmers to easily and quickly find the error.

Advantages of the hexadecimal number system

  • It allows storing more data and information in less space
  • It is very concise
  • It is fast and more straightforward for the computer to understand
  • It can be easily converted into binary form.
  • It can be used to write the long binary value in short.
  • It is more user-friendly.
  • The grouping of digits makes it easier to understand by the programmers
  • Writing fewer digits reduces the possibility of errors in the code.

Disadvantages of the hexadecimal number system

  • Challenging to understand by ordinary people or beginners
  • Hard to perform arithmetic operations like multiplication and division on them
  • Most difficult number system for handling the computer's data
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