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Hexadecimal numbering is a basic and important concept in computing and digital electronics. The hexadecimal numbering system which is often abbreviated as “hex”, is a much more condensed view than binary or decimal. This article will take you through the basics of the Hexadecimal numbering System – from Introduction and Terminologies. Among other things, we will try to understand why every kind of stuff (memory addressing in particular and modern web design – hexa rgba rgb) applies hexadecimal numbers so broadly. Furthermore, we will explain how to convert hexadecimal into other numbers and vice-versa using illustrative examples step-by-step. Finally, you will have a firm understanding of what hexadecimal numbers are and why they matter for our everyday technology. Primary TerminologiesHexadecimal Numbers consist of many unique terminologies that we should know. 1. Numbering System: The numbering system is a kind of way where you figure out how to represent numbers using particular symbols. Such options are of, for example; binary (base-2), decimal system(base-10) or hexadecimal base16]). Any system has to count and represent numbers in a particular way. 2. Base: The number of distinct symbols used by the system is what we mean when referring to its base. The decimal number system, uses base-10 ( with ten symbols 0 through 9 ) while the hexadecimal is based on sixteen digits from ‘0-9’ to ‘A-F’. The base is the key to finding out the place value of each digit in a number. 3. Digit: It is a single symbol that represents one of the values in a numbering system. Hexadecimal uses 0-9 and A-F for numbers (where A is 10, B is 11 and so on up to F, the letter F means digit with number of 15). In a number, value of the digit will be defined based on its position with respect to that base. 4. Conversion: Conversion is the method of changing a number from one base to other. This is important to know for relating between different numbering systems. One might be converting a 32-bit hexadecimal number to its decimal representation by multiplying each of the four-bytes (8-characters) it has with 16 raised to certain power and adding the result. The opposite approach follows analogy: changing from decimal to hexadecimal, we divide the number by 16 repeatedly and recording its remainders. Hexadecimal Numbering SystemThe Hexadecimal numbering system, or base-16 system is a way of counting similar to the binary number on how we represent numbers but uses sixteen distinct symbols: 0-9 and A-F where A stands for 10, B for 11 up until F that represents fifteen. This numbering system has a very important place in computing because it provides a shortened version of representing binary data for reading and writing. Programmers, digital electronics people and computer engineers use hexademical numbers in places like addressing memory locations or defining colors to be used by HTML in web designs. It generally just goes along well with the bitwise operations. Hexadecimal simplifies the conversion of binary groupings of four digits to a single hexadecimal digit, which in turn makes interpreting and working with binary code easier than it could be otherwise. Visual RepresentationFollowing is the table of Hexadecimal Number systems with its equivalent values of Decimal Numbers and 4-Bit Binary Number.
Why Hexadecimal?There are several reasons to why hexadecimal is favored in computers. Firstly, hex is a far more concise, compact and readable way to display binary data. For exemple, ‘ 11110000 ‘ in binary can be stored as high-density as possible if it’s written like ‘ F0 ‘ in hex. The compact form is readable and makes hex code less error prone. Secondly, hexadecimal works well with binary systems since each digit of a hex corresponds to four digits in the corresponding bin value making conversions easy. Additionally, hexadecimal is highly used in programming and digital electronics from memory addresses to color codes of colors in web design. This makes the hexadecimal digits an invaluable tool in technology due to their efficiency and convenience. Hexadecimal and Decimal ConversionConversion of Hexadecimal to DecimalThe basics of the conversion between decimal and hex are probably one of the most basic thing in computing. The way of conversion from hexadecimal to decimal is, each digit of decimal is multiplied by 16 raised to the power of its position starting at the rightmost side which is zero. Afterward, sum these multiplications in order to get the decimal value. Example: Convert (1A3)16 to decimal.
Example: Convert (A7B)16 to decimal.
Conversion of Decimal to HexadecimalSimilarly, for converting decimal number to the hexadecimal, the decimal number is repeatedly divided by 16 and recording the remainders for each division. Therefore, simply read these remainders from the bottom to top, to get a hexadecimal equivalent. Conversion like these are important to understand and implement hexadecimal in various computing applications. Example: Convert (419)10 to hexadecimal
Example: Convert (92)10 to hexadecimal
ConclusionHexadecimal numbers are widely used in coding and digital electronics because they compactly represent binary data and can handle large datasets. Knowing hexadecimal is essential for memory addressing, writing code, and understanding computer science concepts, including web color codes. People who understand hexadecimal often find it easier to read, write, and understand data. Hexadecimal remains crucial in firmware, memory controllers, and various tech fields, regardless of which processor company is leading. Frequently Asked Questions on Hexadecimal Numbering – FAQsWhy would a programmer use hex over binary?
Why do we use Hexadecimal in digital electronics.
How does Hexadecimal involves in addressing the Memory?
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Reffered: https://www.geeksforgeeks.org
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Category: | Coding |
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