Hex to Binary

Hexadecimal System (Hex System)

The hexadecimal system, also known as base-16 numbering system, is a mathematical notation that uses 16 digits to represent numerical values. The system uses the digits 0 through 9 and the letters A through F to represent the numbers 10 through 15, respectively.

In the hexadecimal system, each digit represents a power of 16, starting with 16^0 on the rightmost digit and increasing by a power of 16 as you move to the left. For example, the hexadecimal number "3A7" can be expanded into decimal form as follows:

3A7 = (3 x 16^2) + (10 x 16^1) + (7 x 16^0) = (3 x 256) + (10 x 16) + (7 x 1) = 984

Hexadecimal numbers are commonly used in computer science and digital electronics because they can be easily converted to and from binary, which is the language that computers use to represent information. In fact, each hexadecimal digit corresponds to a four-bit sequence in binary, allowing for easy conversion between the two systems.

Hexadecimal notation is often used to represent memory addresses, color codes, and other numerical values that are too large or too cumbersome to represent in decimal or binary form.

4 binary digits, which is also known as nibbles make up half a byte. This means one byte can carry binary values from 0000 0000 to 1111 1111. These binary digits can be represented in HEX in a more friendlier manner, ranging from 00 to FF.

If you are familiar with computer programming, you will often see colors being represented by a 6-digit hexadecimal number; e.g., FFFFFF for white and 000000 representing black.

Related Tools: Text-to-binary converter | Binary-to-HEX Converter | Binary to ASCII | ASCII to binary

How to Convert Hex to Binary System

Converting hexadecimal numbers to binary is relatively simple, as each hexadecimal digit corresponds to a four-bit binary sequence. To convert a hexadecimal number to binary, you simply need to replace each hexadecimal digit with its corresponding four-bit binary sequence. Here's an example:

Let's say we want to convert the hexadecimal number "5A" to binary. We can do this by replacing the digit "5" with its binary sequence "0101" and the digit "A" with its binary sequence "1010", giving us:

5A = 0101 1010

As you can see, each hexadecimal digit is replaced by four bits of binary, giving us a total of eight bits (or one byte) in binary.

If the hexadecimal number has a fractional part, you can convert it to binary by multiplying the fractional part by 16 and repeating the process until the fractional part becomes zero or until you've reached the desired level of precision. For example, the hexadecimal number "3.2A" can be converted to binary as follows:

3.2A = 0011 . 0010 1010 = 0011 . 0010 1010 0000 0000 0000 0000...

In this case, we simply replaced the digit "3" with its binary sequence "0011", the digit "2" with its binary sequence "0010", and the digit "A" with its binary sequence "1010". We then multiplied the fractional part "0.2A" by 16 to get "3.4", which we converted to binary in the same way. We can repeat this process as many times as we need to achieve the desired level of precision.

The basis of computer networks, software engineering are hexadecimal and binary digits. Converting from a hexadecimal to a binary number is very common because base 16 offers a clean way to express four base 2 digits for each base 16 used, making it much easier to read.