Basics of HexadecimalIt has become clear from a number of your questions that quite some of you are unfamiliar with the hexadecimal device, or truely, hex

 The hexadecimal machine is used Basics of Hexadecimal:

throughout computing and if you have by no means studied this Base16 numering machine, it can appear exceedingly opaque Basics of Hexadecimal.

​For the ones of you who may also have been beaten through this seemingly mysterious numbering device, I commit this quick advent and evaluate of the hexadecimal numbering machine.

​As you understand, you come across the hexadecimal machine throughout your pc and software program. It normally looks some factor like this 0x4D or without a doubt 4D. without delay, you recognize something is unique right here because first, it regularly starts offevolved with that extraordinary 0x, and second, there are letters in there and not just the digits (0-9) Basics of Hexadecimal.

​we are able to frequently stumble upon hex in difficult drive photographs consisting of in digital forensics consisting of underneath.

​Or we might also encounter hex even as the use of Wireshark, like below.

​And we are very probable to stumble upon hex in analyzing our IDS alerts together with in laugh, like that underneath.

​some of the most critical motives to recognize and look at hex is that our MAC addresses on all NICs and community devices are all in hex, and IPv6 will ALL be in hex, once it’s far widely followed.

​​in case you are not familiar with hex, this is the time to take a couple of minutes to try and recognize it. a couple of minutes now will in all likelihood prevent hours of headaches later Basics of Hexadecimal.

​Our Decimal gadget
​
one of the great ways to come back to recognize the Base16 or hexadecimal device is to go again to the fundamentals of a numbering system you’re very familiar with, the Base10, or decimal system. In that gadget, we’ve 10 digits (zero-9) and every column in that system represents a value 10 times extra than the one to the right of it. So, for instance Basics of Hexadecimal:

​31337

​Represents (beginning on the proper and shifting left):

​7 ones (1)
3 tens (10)
3 loads (one hundred)
1 thousand (one thousand)
3 ten hundreds (10,000)

​each place holder is 10 instances larger than the preceding one. The hex device works similarly, however each column is sixteen instances large than the previous column. So, the primary 4 hex columns have values like this:

​4096 256 sixteen 1

​each is sixteen instances more than the column to its right Basics of Hexadecimal.

​The Hex Numbering gadget
​
The hex machine is a base16 numbering gadget. like the decimal or Base10 system, the hex machine has to have sixteen digits to cowl all the possibilities. sadly, we most effective have 10 to paintings with (zero-nine), so we need to add six greater. The pc industry has decided to use the letters A-F to represent these additional values. which means that the hex system has the subsequent values Basics of Hexadecimal.

​

zero = 0
1= 1
2 = 2
three = 3
4 = four
five = 5
6 = 6
7 = 7
8 = 8
nine = 9
A = 10
B = 11
C = 12
D = 13
E = 14
F = 15

​because of this whilst we see a hex illustration of more than a few which includes:

​0x45

​we are able to examine it similarly to a decimal number except the second one column represents 16s and now not 10s. which means that 0x45 in hex may be evaluated along with:

​5 x 1 = 5
4 x 16 = sixty four
—————
= sixty nine

​If we’ve got a hex wide variety along with DE, we will calculate its value this way:

​D represents thirteen x sixteen = 208
E represents 14 x 1 = 14
————————————–
= 222

​​

Why We Use Hex
​
In computing, a chunk is a unmarried on/off switch often represented by a 0 or a 1. A byte is 8 bits often represented by means of 0000 0000. A byte is an vital unit in computing because it regularly used to symbolize an ASCII man or woman or a single octet in an IP cope with, amongst many different things. The variety of numbers that one byte can constitute is zero-255 or 256 values. this is why in our IPv4 addresses, every octet (byte) has a fee from zero-255, such 192.168.zero.254 with a netmask of 255.255.255.zero. follow me?

​most human beings have a hard time operating in the Base2 system that underlies our computer structures. Base2 numbers might be represented like this Basics of Hexadecimal:

​1101 1100

​Athough this wide variety represents 2220 in decimal, the conversion to decimal isn’t always simple or intutive.

The hex machine allows us to symbolize the values of a single byte with just digits as the two digit hex values also variety from 0 – 255. Hex is more compact than the Base2 machine and it looks and acts lots extra just like the decimal gadget than Base2. similarly, every price that can be represented by way of a byte may be represented in hex by means of the values among 0x00 – 0xFF (255) Basics of Hexadecimal.

​Hex Math 
​
likely the easiest way to do hex math is to apply the calculator constructed into every windows device. Open the windows calculator like underneath:

​​Now, visit the View menu at the pinnacle and select “Programmer”.

​As you could see on the left aspect of the calculator approximately halfway down, there are four buttons, Hex, Dec, Oct, Bin. by way of default, it ought to be set to Dec or Decimal, our familiar Base10 gadget. If I want to go into a hexadecimal variety, truly click on on Hex and then input the number.

​​when I accomplish that, i’m able to then toggle to the Dec button and it’s going to convert my hexadecimal wide variety to a decimal wide variety Basics of Hexadecimal.

​​eventually, if we need to feature, subtract, multiply or divide in hex, we are able to use the Programmer view inside the Calculator as nicely. this is, is we desired to feature the hex cost DE to the hex price A5, we definitely input DE inside the calculator press the addition (+) after which input the A5 after which press equal. The end result could be 183 in hex Basics of Hexadecimal.

​​after which we are able to toggle to the Dec button and get the decimal equivalent or 387.

​​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.

Hexadecimal Number System Table
Below is the table of hexadecimal number systems with equivalent values of the binary and decimal number systems Basics of Hexadecimal.

Decimal Numbers 4-bit Binary Number Hexadecimal Number

0 0000 0
1 0001 1
2 0010 2
3 0011 3
4 0100 4
5 0101 5
6 0110 6
7 0111 7
8 1000 8
9 1001 9
10 1010 A
11 1011 B
12 1100 C
13 1101 D
14 1110 E
15 1111 F
Below is the link to download the table. Students can download the PDF and learn offline too.

Download PDF – Hexadecimal Number System
Hexadecimal Number System Conversions
As we know, there are 16 digits in the hexadecimal number system, represented from 0 to 9 same as decimals, but after that, it starts with an alphabetical representation of preceding numbers such as A, B, C, D and E. Let us see the conversion of ‘hex’ into other number systems.

Hexadecimal to Decimal Conversion
Here, you will see the representation of a hexadecimal number into decimal form.

Hexadecimal

0 1 2 3 4 5 6 7 8 9 A B C D E F
Decimal 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
15

Decimal to Hexadecimal Conversion

You have learned how to convert hexadecimal numbers to decimal numbers. Now let us find out how we can convert a decimal number into a hexadecimal number system. Follow the below steps:

Firstly divide the number by 16
Take the quotient and divide again by 16
The remainder left will produce the hex value
Repeats the steps until the quotient has become 0
Example: Convert (242)10 into hexadecimal.

Solution: Divide 242 by 16 and repeat the steps, till the quotient is left as 0.

decimal to hexadecimal number system

Therefore, (242)10 = (F2)16

Hexadecimal to Octal Conversion
Here, you will see the representation of a hexadecimal number into octal number form.

Hexadecimal

0 1 2 3 4 5 6 7 8 9 A B C D E F
Octal 0 1 2 3 4 5 6 7 10 11 12 13 14 15 16
17

Octal to Hexadecimal Conversion
To convert octal to hex, we have to first convert octal number to decimal and then decimal to hexadecimal. Let us understand it with the help of an example;

Example: Convert (121)8 into hexadecimal.

Solution: First convert 121 into decimal number Basics of Hexadecimal.

⇒ 1 × 82 + 2 × 81 + 1 × 80
⇒ 1 × 64 + 2 × 8 + 1 × 1
⇒ 64 + 16 + 1
⇒ 81

(121)8 = 8110

Now converting 8110 into a hexadecimal number.

decimal to hexadecimal

Therefore, 8110 = 5116

Hexadecimal to Binary Conversion
Here, you will see the representation of a hexadecimal number into binary form. We can use only 4 digits to represent each hexadecimal number, where each group has a distinct value from 0000 (for 0) and 1111 (for F= 15 =8 + 4 + 2 + 1).

Hexadecimal

0 1 2 3 4 5 6 7 8 9 A B C D E F
Binary 0 1 10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 1110
1111

Binary to Hexadecimal Conversion
Binary to hexadecimal conversion is a simple method to do. You just have to put the values of the binary number to the relevant hexadecimal number.

Example: Convert (11100011)2 to hexadecimal.
Solution: From the table, we can write, 11100011 as E3.

Therefore, (11100011)2 = (E3)16

Facts of Hexadecimal Number System
Out of many types of number representation techniques, the Hexadecimal number system is one having a value of base 16.
So Hexadecimal numbers have 16 symbols or digital values, i.e 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.
A, B, C, D, E, F are single bit representations of 10, 11, 12, 13, 14 and 15 respectively.
The addition of either an o prefix or an h prefix indicates Hexadecimal.
A power of 16 is the weight of the position of every digit.
Solved Examples on Hexadecimal number system
Example 1: What is 5C6 (Hexadecimal) Basics of Hexadecimal?

Solution: Step 1: The “5 “ is the “16 x 16” position, so that means 5 x16 x16

Step 2: The ‘C’ (12) is in the “16” position, so that means 12 x 16.

Step 3: The “6” in the “1” position so that means 6.

Answer is : 5C6 = 5 x 16 x 16 + 12 x 16 +6 = (1478 ) in Decimal.

Example 2: What is 3C5 (Hexadecimal)?

Solution: Step 1: The “3 “ is the “16 x 16” position, so that means 3 x16 x16

Step 2: The ‘C’ (12) is in the “16” position, so that means 12 x 16.

Step 3: The “5” is in the “1” position so that means 5.

Answer is : 3C5 = 3 x 16 x 16 + 12 x 16 + 5 = (965) in Decimal.

Example 3: What is 7B5 (Hexadecimal)?

Solution: Step 1: The “7 “ is the “16 x 16” position, so that means 7 x16 x16

Step 2: The ‘B’ (11) is in the “11” position, so that means 11 x 16.

Step 3: The 5” in the “1” position so that means 5.

Answer is : 7B5 = 7 x 16 x 16 + 11 x 16 +5 = (1973) in Decimal.

Example 4: What is 2E8 (Hexadecimal)?

Solution: Step 1: The “2 “ is the “16 x 16” position, so that means 2 x16 x16

Step 2: The ‘E’ (14) is in the “16” position, so that means 14 x 16.

Step 3: The “2” is in the “1” position so that means 2.

Answer is : 2E8 = 2 x 16 x 16 + 14 x 16 +8 = (744) in Decimal.

Example 5: What is 4F8 (Hexadecimal)?

Solution: Step 1: The “4 “ is the “16 x 16” position, so that means 4 x16 x16

Step 2: The ‘F’ (15) is in the “16” position, so that means 15 x 16.

Step 3: The “8” is in the “1” position, which means 8.

Answer is : 4F8 = 4 x16 x 16 + 15 x 16 +8 = (1272) in Decimal.

Practice Questions
What is 5D16 in decimal number?
Convert decimal number 21 into a hexadecimal number.

What is 01101112 in hexadecimal?

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Binary Number System
Octal Number System
Hexadecimal Calculator
Number System For Class
Important Questions Class 9 Maths Chapter 1 Number System
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Frequently Asked Questions – FAQs
What is a hexadecimal number system?
The hexadecimal number system is a number system with base-16. It is represented by only 16 digits or values.What are the 16 digits of the hexadecimal number system?

The 16 digits of the hexadecimal number system are 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.
What is the use of the hexadecimal number system?
Hexadecimal number systems are used for computer programming and designing. Since the computer understands only binary digits (0 and 1), thus each hexadecimal digit represents four binary digits.
What is 3CD (hexadecimal) Basics of Hexadecimal?

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