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.

• 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.

• 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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