Definition
The hexadecimal number system is a type of number system, that has a base value equal to 16. It is also pronounced sometimes as ‘hex’. Hexadecimal numbers are represented by only 16 symbols. These symbols or values are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F. Each digit represents a decimal value. For example, D is equal to base-10 13.
Hexadecimal number systems can be converted to other number systems such as binary number (base-2), octal number (base-8) and decimal number systems (base-10). The concept of the number system is widely explained in the syllabus of Class 9.
The list of 16 hexadecimal digits with their equivalent decimal, octal and binary representation is given here in the form of a table, which will help in number system conversion. This list can be used as a translator or converter also. 1
Example
Here we will see example of how to calculate Decimal Equivalent of Hexadecimal number
Hexadecimal Number: 19FDA16
19FDE16 can be written as 19FDA
Step 1: (1 × 16⁴) + (9 × 16³) + (15 × 16²) + (13 × 16¹) + (10 × 16⁰) =
Step 2: (1 x 65536) + (9 x 4096) + (15 x 256) + (13 x 16) + (10 x 1)
Step 3: (65536+ 36864 + 3840 + 208 + 10) 10
Step 4: (106458)₁₀ or 106458
References
1 “What Is Hexadecimal Numbers System? Table, Conversions, Examples”. 2022. BYJUS. https://byjus.com/maths/hexadecimal-number-system/.
Additional Reading
“Arithmetic Operations Of Hexadecimal Numbers – GeeksForGeeks”. 2020. GeeksForGeeks. https://www.geeksforgeeks.org/arithmetic-operations-of-hexadecimal-numbers/.
Justice, Dalton. 2014. “Hexadecimal”. SlideServe. https://www.slideserve.com/dalton/hexadecimal.
Videos
It is really important to understand the reason for using Hexadecimal and Octal number systems. In this video, I have explained the need, various usages of Hexadecimal and Octal number system, and also conversion between binary, hexadecimal, and octal number system.
⭐ I suggest that you read the entire reference. Other references can be read in their entirety but I leave that up to you.
Mathematical Mysteries 