Hexadecimal system of numbers is widely used along with binary and octal numbers in computer science. Hexadecimals include the 10 digits 0 to 9, the letters A, B, C, D, E and F to represent the numbers from 10 to 15. In computer coding, two hexadecimal representation ranging from 00 to FF can efficiently replace a byte consisting of 8 binary bits. Hexadecimal coding is also considered to be relatively human friendly, when compared to long strings of binary coding. 
The place value chart for Hexadecimal system of numbers is given below:
The place value of each position in hexadecimal system is 16 times the place value of the immediate position to its right.
Let us look into how the decimal numbers are represented in Hexadecimal system. Each digit of the number is multiplied by its place value and the products are added to get the number in decimal system. For letters A, B, C, D, E and F, the corresponding numbers are used for multiplication.
Consider the Hexadecimal number 5F23A.
The correspondence between the digits and the face value are as follows:
5 F 2 3 A
16^{4} 16^{3} 16^{2} 16^{1} 16^{0}.
Thus, 5F23A = 5 x 16^{4} + 15 x 16^{3} + 2 x 16^{2} + 3 x 16^{1} + 10 x 1 = 327,680 + 61,440 + 512 + 48 + 10
5F23A_{16} = 389,690_{10}.
The hexadecimal system provides more compact representation for larger numbers than the decimal system.
The decimal form of a hexadecimal representation is the sum of the products of its digits and their corresponding place values. Let us look at the example.
Let us write B13F_{16} into its Decimal form.
Each digit is multiplied by its place value and the products are added to get the decimal equivalent of the number.
B13F_{16} = B x 16^{3} + 1 x 16^{2} + 3 x 16^{1} + F x 16^{0}
= 11 x 4096 + 256 + 48 + 15
= 45,375_{10}
The method applied to convert a decimal to hexadecimal is similar to that which is followed to convert a binary number to a decimal. Divide the number and the successive quotients by 16. Arrange the remainders got in reverse order to get the hexadecimal number.
Let us find the hexadecimal equivalent for 1875_{10}.
The remainders in each step of division are 3, 5 and 3, reversing the order of which, we get the hexadecimal representation as 753.
1875_{10} = 753_{16}
While adding hexadecimal numbers, the sums exceeding 16 are carried over as 1.
Let us add A6B_{16} and 34C_{16}
1 < Carried over digit A 6 B + 3 4 C  D B 7 
As B and C correspond to 11 and 12, we essentially add 11 + 12 = 23 for adding B + C. 16 is subtracted from 23 and carried over as 1 to the next place and the difference 7 is written below.
Similar borrowing rules are applied in subtraction. 16 is borrowed from left, if the digit subtracted is greater.
Let us subtract 4A3_{16} from 2B5_{16}
16 16 < Borrowed numbers ^{3}4^{9}A3  2 B 5  1 E E 
As 5 is greater than 3, to perform subtraction, 16 is borrowed from left. 16 + 3  5 = 14 which is written as E. After the borrow, digit 9 is left in the place of A. So, to subtract B, 16 is again borrowed from the the left. 16 + 9  B = 25  11 = 14 which is again E. As 1 is used for borrow, 3 is left in the place of 4. 3  2 = 1.
Multiplication is carried out digit wise and the products are added as done with decimal numbers.
Let us multiply A2_{16} and 1B_{16}.
First, each digit in A2 is multiplied by B. 2 x B = 2 x 11 = 22, which is 16 in hexadecimal form. The digit 1 is carried over and added to the product A x B = 110 + 1 = 111, which is written as 6F. Addition rules are followed as explained earlier. The following chart gives Binary and hexadecimal representation for the decimal numbers 0 to 31.
Decimal 
Binary  Hexadecimal 

Decimal 
Binary 
Hexadecimal 
0 
0000  00 
16 
10000  10 

1 
0001 
01 
17 
10001 
11 

2 
0010 
02 
18 
10010 
12  
3 
0011 
03 
19 
10011 
13 

4  0100 
04 
20 
10100 
14 

5 
0101 
05 
21 
10101 
15 

6 
0110 
06 
22 
10110 
16 

7 
0111 
07 
23 
10111 
17 

8 
1000 
08 
24 
11000 
18 

9 
1001 
09 
25 
11001 
19 

10 
1010 
A  26 
11010 
1A 

11 
1011 
B 
27 
11011  1B 

12  1100  C  28  11100  1C  
13  1101  D  29  11101  1D  
14  1110  E  30  11110  1E  
15  1111  F  31  11111  1F 