Hexadecimal

**Hexadecimal:**

• It is commonly known as ‘hex’

• It is a base 16 number system.

• It uses 16 digits values to represent each digit.

• For the first ten digits from 0 to 9, it uses the same numbers.

• However, for 10 to 15 it makes use of A to F.

• That is,

**A=10, B=11, C=12, D=13, E=14, F=15**.• It follows the same rule as binary and denary numbers with base 16x.

• For a typical 5-digit hex number, the headings will be,

• 16 equals 24 meaning that, a hex number can be represented in binary using four bits.

### Example:

## 25 |

• Here, ‘H’ represents the hex prefix.

### Why Use Hexadecimal Number System?

• On daily use, it is not convenient to interact in binary numbers for humans.

• As a result, a more convenient way was needed.

• A byte contains 8-bits and represents values 0000 0000 to 1111 1111 (0 to 255).

• The 8-bits of a byte are divided into two groups i.e. top 4 bits and low 4 bits.

• The 4 bits of a byte can give values from 0 to 15 therefore, a base 16 number system was introduced.

• Using the base 16 representation, a byte can be represented by 2 hex digits instead of 8-bits.

• Working through a binary number with base 16 is much easier.

• E.g. If you have AF, you can determine its value by simple multiplication (10 x 161 + 15 x 160) = 75 or 0100 1011.

### Binary to Hexadecimal Conversion:

• Let’s take an example binary number, 1 0 0 0 0 1 1 1 1 1 1 1 0 1.

• Starting from right to left, group it into sets of 4 bits. _ _10 0001 1111 1101

• If the last set doesn’t make 4 bits, add 0s that will make it, 0010 0001 1111 1101

• Now find out the values of each set individually and then combine the digits.

• Combine the converted hex digits together i.e. 21FD.

### Hexadecimal to Binary Conversion:

• Consider an example hex number, BF08.

• Find the equivalent 4-bit binary representation of each hex digit.

• Combine the 4-bits groups together i.e. 1011111100001000.

### Hexadecimal to Denary Conversion:

• To convert a hex number to denary, multiply each digit with its value.

• Consider the number, C8F.

• Add these numbers together to get the denary value of the hex number i.e. 3072 + 128 + 15 = 3215.

### Denary to Hexadecimal Conversion:

• Just like denary to binary, denary to hexadecimal conversion can be done with any of the two methods i.e. ‘try and error’ and ‘repetitive division.

### Method 1 – Try and Error:

• Consider the denary number 2004.

• Try to place hex digits below 162, 161 and 160 and to find the hex representation.

• As compared to denary to binary, denary to hex ‘try & error’ method is much more complex.

• This table show, the denary number 2004 is 7 lots of 256 (1792), 13 lots of 16 (208) plus an extra 4.

### Method 2 – Repetitive Division:

• In this method, the number required to be converted in hex is divided repetitively with 16.

• The remainder is then read from bottom to top.

• Let’s take 2004 in denary and convert it into hexadecimal.

**Uses of Hexadecimal Numbers**

### Memory Dumps:

• A hex number system is often used when new software is developed to trace errors.

• The computer memory can solve many problems.

• Memory dump can be represented as the memory content that is the output to a monitor or a printer.

• The figure above shows the memory location on the far-left side and hex codes against these memory locations.

• Developers can determine errors from these hex codes to find out where in the memory the fault occurs.

• Tracing errors using hex numbers is very efficient compared to the binary numbers.

• A hex number system is a powerful tool for fault and error tracing, but it requires computer architect knowledge.

### HTML (HyperText Mark-up Language):

• It is a language that is most often used to make the text more presentable. E.g. to change the color.

• It uses to bracket pieces of codes. E.g. marks the start of the code cell and ends it.

• Whatever is written between and is defined.

• Different hex values represent different colors:

• The hex value for any color can be generated and there are some websites available that allow the user to generate HTML code for any color.

### MAC Address (Media Access Control):

• The MAC Address represents a unique number that helps in identifying any device on the internet.

• It is 48 bits number i.e. represented by 6 groups of 12 hex numbers. E.g. NN-NN-NN-DD-DD-DD or NN:NN:NN:DD:DD:DD.

• The first of this number represents the manufacturer ID and the second half represent the device’s serial number.

• Sometimes lower-case hex numbers are also used in the MAC address.

• It is a Network Interface Card (NIC) of the device.

### Examples of Manufacturer Identity:

### Web Addresses:

• The ASCII codes of the characters typed through a keyboard can also be represented using the hex values.

• One example of the use of ASCII code is the URL or web address

### Assembly Code & Machine Code:

• The 8-bit computer registers have the largest number 1111 1111 (8-bits).

• The hex representation of this largest number is FF.

• The computer uses 8-bit binary numbers but for programmers’ convenience assembly language is used which uses hex numbers.

• In assembly language, hex value can be moved using command MOV.

• E.g. MOV AX, 03 where AX represents the register and 03 is the value that will be moved to the register.