The Denary, Binary & Hexadecimal Number Systems In Computer Science there are 3 numbering systems used to represent data:

• Binary (Base 2)
• Denary (Base 10)
• Hexadecimal (Base 16)

Binary System

• Whatever the type or format of the data, in computer it is communicated as 1s (on) and 0s (off)
• To process data that can be of any type (i.e., text, numbers, image, audio), language (English, Arabic etc.) etc must be first converted to the binary system or language to be able to get process by computer or computer processor, more precisely
• Binary system is a computer language which has only two alphabets i.e., 0 and 1
• 0 represent not or off or negative or false or any synonym of these mentioned words
• 1 on the other hand represents yes or on or positive or true or again any synonym or these words
• Together both the 0s and 1s are represent or called as bits the name extracted from Binary Digits
• Bit can be considered as atom of a computer (the smallest unit either 1 or 0) but this smallest unit (like we study in Chemistry) get combined with other units (0s or 1s) and form data which can be of a size from very small to very large in numbers
• It is only the binary language that uses within the computer to perform operations hence every data needed to be converted before and after the operations
• 2 is the base for the binary system of numbers

Denary System

• Denary or decimal system is the most common system of our daily life even other than computer.
• The denary system uses the most common numbers, the numbers from 0 to 9 and hence has a base of 10 for representation.
• This system of numbers in mathematics can be used to represent any class of numbers like natural numbers, whole numbers or fractions etc.

Hexadecimal System

• Like binary and denary number system the hexadecimal is another number system widely used in computer for some typical purposes.
• As from the name hex (6) and decimal (10) this number system based on 16 numbers and hence has a base of 16.
• Numbers 0 to 9 are from decimal or denary numbers and additional 6 numbers either 11 to 15 or A to F in alphabets.
• In some cases, hexadecimal number seems more convenient when small size numbers or codes can be used to represent typical identities like codes for memory dumps or colour codes in HTML.
• Hence, unlike large numbers in quantity in binary or denary, hexadecimal is a good replacement for ease of numbering representation.
• So huge numbers of binary which are difficult to read/write/remember/explain to humans, hexadecimal make relatively easy for computer engineers or scientists to deal with it.
• Where in binary 1 digit represent 1 bit, a single digit of hexadecimal represents four bits.

Uses of Hexadecimal Systems:

Memory addresses:

• Memory address are the address for memory written with the combination of two hexadecimal numbers.
• The first hexadecimal number on the left side is for the segment while the number on the right side is for offset.
• A404:2 is an example of such number use for memory address.

Colour codes in HTML:

• The use of this number system is very popular as in colour codes used in HTML or CSS.
• Any colour in RGB (Red Green Blue) have a unique representation in hexadecimal.
• For example, the colour code of yellow is #FFFF00 while for Brown colour the code in HTML is #964B00

Codes for error messages:

• Typical codes are assigned to typical errors just like code language in any industry.
• This helps engineer to refer to the exact problem easily.
• For example, code “ASF_E_ALREADYINITIALIZED” has a unique hexadecimal code “0xC00D07F7L” which describe initialization of the entity; hence rejecting any change/alteration in settings. See the list of error code in Microsoft.com.

Memory dumps:

• Like a black-box in airline industry, memory dumps are dumped codes that computer stores at the time of crash.
• These dumped codes are a record of what was behind that crash.
• Using small codes of hexadecimal at the time of crash (when the time is too short for complete log) computer direct the computer engineers or scientists to the exact memory location.

URLs in Internet:

• Spaces are not acceptable in URL (Uniform Resource Locator) more commonly known as web address, address to the location of a web resource which we write/type in the address bar of a web browser.
• Any space in the web address replaced by the % (sign of percentage) followed by a hexadecimal number 20.
• Together %20 is a replacement of space inside a URL.
• [https://a3education.com/Computer Science] would be [https://a3education.com/Computer%20Science].

Assembly language:

• Like codes for typical error messages, hexadecimal numbers also used to replace large numbers of binary for typical instruction or data codes while writing assembly language.
• This helps the programmer a lot as it not only saves the time but the effort and length of the code as well

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