What is Hexadecimal Numbering? – Explained

As we know, numbers always make magic. Hope, you have felt the same. To get effective support on numbering, continue with this blog.

What is hexadecimal?

In the year 770 AD, Hex, represents the term “hexadecimal base counting,”. This was effectively invented in France. Whereas, Mervin, a famous expert, who has become a counsellor to King Charlemagne during the time- because he had eight fingers on each hand.

Whereas, Hexadecimal is the set of numbering systems – which has a base of 16. In accordance with this, it can be used to signify large numbers with fewer digits.

According to this system, it has 16 symbols or conceivable digit values from 0 to 9, trailed by six sequential characters – for example: A, B, C, D, E, and F. These characters are highly utilized to characterize decimal values from 10 to 15 in single bits.

Hexadecimal represented as:

Hexadecimal is identified as Base 16 or hex – which is best among the four effective numbering systems.

Whereas, the other three are decimal (base 10), binary (base 2), and octal (base 10).
Here’s what the decimal and hexadecimal systems look like for digits 0 to 15.

The hexadecimal system is the representation of sequential numbers as base units. Even if it includes 0. The first nine numbers (0 to 9) are the same ones usually used in the decimal system. Furthermore, the six two-digit numbers (10 to 15) are shown as letters A through F. And, this is the best way to demonstrate how the hex system utilizes the numbers from 0 to 9. This in fact helps to find the capital letters A to F to characterize the equivalent decimal number.

As per the numbering system, every digit’s position is 16 times more substantial than the digit mentioned in the previous position. Eventually, the hex number begins with the least significant digit on its right-hand side. When it comes to the numeric value of this number, it is calculated by multiplying each digit by the value of its position and by adding the products. Finally, this is the actual procedure of hexadecimal as per the positioning or weighing system.

The need for hexadecimal numbers

When you are using the computing system, the binary string equivalents of any large decimal numbers can provide you with long output. In this case, if it contains 16-bit or 32-bit numbers you may feel difficult to read and mention them without creating errors. Whereas, these problems can be easily rectified by allotting the binary numbers into groups of four bits, i.e., by utilizing the hexadecimal numbering system.

Next, with the support of hex numbers, it is effectively compact than binary numbers because you can represent large binary numbers under fewer digits. Finally, they are easier to recognize than long binary strings of 1s and 0s.

What is the difference between binary and hexadecimal numbering?

You may have seen the vital difference between the two numbers is that binary utilizes only two digits: 0 and 1, whereas the decimal makes use of ten digits from 0 to 9. The binary, decimal, and hexadecimal equivalents. You may have a question, why should we prefer the hexadecimal system? as it is a representation of every byte (i.e., eight bits) as two consecutive hexadecimal digits rather than the eight digits required by binary (i.e., base 2) numbers and the three digits needed by the decimal, the hexadecimal system is often used by programmers to define memory locations.

The major effective reason is that hex is highly shorter and more user-friendly to read for humans than binary. At the same time, it is highly easy to convert hexadecimal numbers into binary, octal, and decimal systems. Finally, you may easily prefer the hexadecimal format.

Representation of hexadecimal numbers

In hex, four digits of a binary number are easily represented by a single hex digit. Here, you can divide the binary number into 4-bit sets which means- each set can hold a possible value that can be laid between 0000 and 1111, permitting 16 number combinations from 0 to 15. In accordance with the base value of 16, the maximum value of a digit is 15.

Eventually, it is much better to convert a binary number into a hexadecimal number and vice versa. Whereas, these are the representation of numbers as per the systems.

Add-on, the digits to the left of the hexadecimal point consists of weights 160, 161, 162, and so on. Likewise, the positions to the right represent the weights of 16-1, 16-2, etc.

Example

In order to show the decimal number 512 in hex:

• Decimal value = 512
• 512 = 2×162+0x161+0x160=200
• Hex value = 200
• Hence, the Hex Value is 200 for this question.

Here, we have the example to show the effective conversion of binary and decimal numbers to hexadecimal

Conversion: binary to hexadecimal

In turn, to convert the binary numbers to hexadecimal, four binary digits should be mapped or converted to one hexadecimal digit. Make use of the below terms to see how the conversion works:

Function

• Initially, you need to split the binary value into groups of four, starting from the digit at the far right.
• Match each group of four in contradiction of the consistent hexadecimal value.
• Signify the original binary number in hexadecimal format.

Example

Make use of the conversion from binary number 1011010101100001 to hex form:

Step 1: First, you need to split the binary value into groups of four.

Step 2: Then, replace each set with a hexadecimal value.

Step 3: Finally, showcase the output of the binary as a hex 10110101011000012 = B56116

Conversion-decimal to hexadecimal

In this procedure, while conversion of decimal numbers to hexadecimal- you need to follow the given guidelines

1. Firstly, divide the decimal number by 16.
2. Note down the remainder in hexadecimal form.
3. Now, you have to divide the result by 16.
4. Finally, repeat steps 2 and 3, till you reach the end result of 0.

Note: The hexadecimal value will be shown in the form of a sequence of remainders from the last to the first.

Example

Steps to convert the decimal number 1128 to hexadecimal:

• Step 1: You need to divide 1128 by 16 to reach the result of 70 and the remainder of 8.
• Step 2: Divide the result (70) by 16 to obtain a new result 4 and the remainder 6.
• Step 3: Then, Divide the result (4) by 16 to receive the result of 0 and the remainder of 4.
• Step 4: It shows the representation of a hexadecimal number as the sequence of remainders from the last to the first [112810 = 46816].

What are the Hexadecimal identifiers

Hexadecimal numbers are generally termed prefixed or suffixed with identifiers to escape confusion throughout reading or writing. It makes it easy to differentiate hex numbers from decimal numbers. Some common hex identifiers include:

Some common hex identifiers include:

What are all the Hexadecimal applications?

The hexadecimal numeral system is chiefly useful in computer programming and microprocessors. Developers use it to define colors on webpages, define memory locations for each byte, require certain characters, and more. Hex numbers can also be utilized in microcontrollers to make the procedure simple for handling the data and manipulation.

Other Applications

• Data science and analytics.
• Machine Learning and artificial intelligence.

Hexadecimal advantages and disadvantages

Advantage:

1. Hex numbers are termed to be compact and utilize less memory, since you are enabled to store computer systems.
2. If you have a small size, it can make huge input-output handling in less time when compared with other numbering formats. Because it’s easy to convert hexadecimal to binary and vice versa, the system is widely used in computer programming.
3. On the other hand, it supports representing computer memory addresses.

Disadvantage:

1. The Major drawback of its hexadecimal system is, it is slightly difficult to achieve complex mathematical operations. Which includes multiplication and division.
2. Hex numbers are even termed to be difficult to read and write related to decimal numbers.

FAQ’s