Hexadecimal Numbers

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Hexadecimal Numbers

The one main disadvantage of Binary Numbers is that the binary equivalent of a large decimal number can be quite long, which makes it difficult to both read or write without producing errors especially when working with 16 or 32-bit numbers. One common way of overcoming this problem is to arrange the binary numbers into groups of four as a Hexadecimal Number, starting with the least significant digit at the right hand side. This Hexadecimal or simply "Hex" numbering system uses the Base-16 system with a combination of numbers and letters to represent its Binary or Decimal equivalent.

For example: the following group of numbers 1101 0101 1100 1111₂ are much easier to read and understand than 1101010111001111₂ when all grouped together.

By dividing a binary number up into groups of 4 bits, each group or set of 4 digits can now have a possible value of between "0000" (0) and "1111" (8+4+2+1 = 15) giving a total of 16 different number combinations from 0 to 15, this system is commonly called Hexadecimal, and now q = "16".

The numbers 0 to 9 are still used as in the original decimal system, but the numbers from 10 to 15 are now represented by letters of the alphabet from A to F inclusive and an example of this Hexadecimal system is given below.

Hexadecimal Numbering System

Decimal	4-bit Binary	Hexadecimal
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
16	0001 0000	10 (1+0)
17	0001 0001	11 (1+1)
Continuing upwards in groups of four

Using the original binary number from above 1101 0101 1100 1111₂ this can now be converted into an equivalent hexadecimal number of D5CF₁₆ which is much easier to read and understand than a long row of 1´s and 0´s. Similarly, converting Hex based numbers back into binary is simply the reverse operation.

Then the main characteristics of a Hexadecimal Numbering System is that there are 16 distinct counting digits from 0 to F with each digit having a weight or value of 16 starting from the least significant bit (LSB). In order to distinguish Hexadecimal numbers from Denary numbers, a prefix of either a "#", (Hash) or a "$" (Dollar sign) is used before the actual Hexadecimal value.

Example No1.

Convert the following Binary number 11101010₂ into its Hexadecimal number equivalent.

11101010₂
Group the bits into fours starting from the right hand side
=	1110	1010
=	E	A
Then, the hexadecimal equivalent of the binary number 11101010₂ is #EA₁₆

Example No2.

Convert the following Hexadecimal number #3FA7₁₆ into its Binary equivalent, and also into its Decimal or Denary equivalent.

#3FA7₁₆
	= 0011 1111 1010 0111₂
	= (8192 + 4096 + 2048 + 1024 + 512 + 256 + 128 + 32 + 4 + 2 + 1)
	= 16,295₁₀

Then, the Decimal number of 16,295 can be represented as:-

#3FA7₁₆ in Hexadecimal

0011 1111 1010 0111₂ in Binary.

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External Links about Binary to Hexadecimal Conversion

Practical Guide to Binary, Decimal and Hexadecimal Numbers - Good Tutorial Explains Well.
Niels Jonker

Converting Hexadecimal to Binary - Tutorial about Converting Hex to Binary.
Permadi.com

Converting Binary and Hexadecimal Values - Tutorial about Binary and Hex Conversion.
Computer Hope

Binary to Hexadecimal - Good Tutorial about Binary to Hexadecimal Conversion.
ECAWEB - Educational Computing Association of WA

Binary and Hexadecimal Notation - Tutorial about Binary and Hexadecimal Numbers.
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