Introduction to Hexadecimal

Hexadecimal, often abbreviated as "hex," is a base-16 numbering system used in mathematics and computer science. 

In our daily lives, we use the decimal system, which is base-10. It uses ten digits from 0 to 9.

Hexadecimal, on the other hand, is base-16, which means it uses 16 different symbols. In addition to the usual 0-9 digits, it also includes six extra symbols: A, B, C, D, E, and F. These symbols represent decimal values 10 to 15.

Once a hexadecimal reaches F (16 in decimal) an extra digit is add to the left. (just like we do in decimal when we reach 10.

Hex Counter Demo:

0

Converting hexadecimal to binary

Converting hexadecimal (hex) numbers to binary is a straightforward process because each hex digit directly corresponds to a group of four binary bits (also known as a nibble).

Here's how you can convert a hex number to binary:

1. Write Down the Hex Number

Start by writing down the hexadecimal number you want to convert. For example, let's say you have the hex number "1A."

2. Convert Each Hex Digit individually to Binary: For each hex digit, convert it to its binary representation using the following mapping:

3.Combine Binary Digits

After converting each hex digit, combine the binary representations to form the complete binary equivalent. In our example, "1A" converts to "00011010" in binary.

Let's do the conversion for the hex number "1A":

• "1" in hex is "0001" in binary.
• "A" in hex is "1010" in binary.

Combine these binary values to get the final result: "1A" in hex is "00011010" in binary.

Converting binary to hexadecimal

Converting binary to hexadecimal is simple, we simple do the reverse of the previous example.. Each group of four binary digits (bits) corresponds to a single hexadecimal digit. Here's how you can convert binary to hexadecimal:

1 .Group Binary Digits

Starting from the right, group the binary digits into sets of four, adding leading zeros if necessary to make each group contain exactly four bits.

2. Convert Each Group

For each group of four binary digits, convert it to its equivalent hexadecimal digit using the following mapping:

3. Combine Hexadecimal Digits

Combine the hexadecimal digits obtained from each group to form the complete hexadecimal representation

Binary to hexadecimal example

Binary Number

1101101010101011

1. Group the binary digits into sets of four:

1101 1010 1010 1011

2. Convert each group to hexadecimal

• 1101 (D in hexadecimal)
• 1010 (A in hexadecimal)
• 1010 (A in hexadecimal)
• 1011 (B in hexadecimal)

3. Combine the hexadecimal digits:

The binary number 1101101010101011 is equivalent to the hexadecimal number "DAAB."

Common uses of Hexadecimal

Memory Addressing

Hexadecimal is often used to represent memory addresses in computer systems. Each address corresponds to a specific location in memory, and using hexadecimal makes it easier for programmers and engineers to work with these addresses, especially when debugging or programming low-level software.

Color Representation

Hexadecimal is used in web development and graphic design to represent colors. It's commonly used in HTML and CSS to specify colors by combining red (R), green (G), and blue (B) values in hexadecimal form, such as #RRGGBB or #RRGGBBAA (with an alpha channel for transparency).

MAC Addresses

Media Access Control (MAC) addresses, which are unique identifiers assigned to network devices, are often represented in hexadecimal. A MAC address consists of 12 hexadecimal digits (0-9 and A-F), typically separated by colons or hyphens.

Assembly Language Programming

In low-level programming, assembly languages often use hexadecimal notation to represent machine instructions and memory addresses, making it easier for programmers to write and understand code.

Why do we use hexadecimal?

1. Hexadecimal provides a more compact representation of binary data.

Each hexadecimal digit corresponds to four binary bits (nibble), which makes it easier to work with and read binary values, especially when dealing with large binary numbers.

For example, the binary number 1101101010101011 is represented as D6AB in hexadecimal, which is more concise and human-readable.

2. Hexadecimal is easier to read and remember.

Because hexadecimal contains fewer numbers than binary it is easier for humans to read and remember.