Convert Hexadecimal to Decimal

Here in this page we are going to learn about hexadecimal to decimal conversion.Hexadecimal number is way to represent the number , which base is 16. We are going to convert a number in base 16 to an equivalent number in base 10. It is generally use in digital electronic system. Their are some particular way to covert a hexadecimal number in decimal number.First let us learn about hexadecimal and decmal numbers,then we will learn how to convert.

Hexadecimal number:

Numbers to the base 16 is called as hexadecimal numbers.It uses digits from 0 to 9 and alphabets from A to F.That is it will be a combination of numbers and alphabets.

Examples: 1) 6FDA     2) 2A9B      3) EB2

Decimal numbers:

Numbers with base 10 is called as decimal numbers.Decimal numbers include digits from 0 to 9.Decimal number system is the basic number system and is widely used.

Examples:  1) 25     2) 984        4) 21

 

How to convert hexadecimal to decimal

 

See the below steps -

Step 1: First we find the number of hexadecimal digits in the number.Let there be n numbers.

Step 2: Then we multiply each hexadecimal digit with  16n-1  , when n is equal to number of position from right side.

Step 3: Then we add each number after multiplication.

Step 4: The resultant is equivalent hexadecimal number of the given decimal number.

If the given number contain decimal then

Step 1:Count the number on digits after decimal.Let it be m

Step 2:Then we multiply each digit after decimal with `1/2^m` ,where m is the number of position of digit  from the decimal point.

Step 3: Then we add each number after multiplication.

Step 4: The resultant is equivalent hexadecimal number of the given decimal number.

Converting Hexadecimal to Decimal

 

Below are the examples on converting Hexadecimal to Decimal -

Problem 1:

Convert 7B16 into decimal number.

Solution:

Given hexadecimal number is 7B16.

7B16 = 161 * 7 + 160 * B

= 16 * 7 + 1 * B

= 112 + 1 * 11

= 112 + 11

= 123

Answer is 123.

Problem 2:

Convert 7E16 into decimal number.

Solution:  

Given hexadecimal number is 7E16.

7E16 = 161 * 7 + 160 * E

= 16 * 7 + 1 * E

= 112 + 1 * 14

= 112 + 14

= 126

Answer is 126.

Problem 3:

Convert CA16 into decimal number.

Solution:

Given hexadecimal number is CA16.

CA16 = 161 * C + 160 * A

= 16 * C + 1 * A

= 16 *C + A

=16 * 12 +9

=192 + 9

=202

Answer is 202.

Problem 4:

Convert 2016 into decimal number.

Solution:  

Given hexadecimal number is 2016.

2016 = 2 * 161 + 0 * 160

= 2 * 16 + 0 * 1

= 2 * 16 + 0

= 2 * 16

= 32

Answer is 32.

Problem 5:

Convert 2416 into decimal number.

Solution:  

Given hexadecimal number is 2416.

2416 = 2 * 161 + 4 * 160

= 2 * 16 +  4 * 1

= 2 * 16 + 4

= 32+ 4

=36

Answer is 36.

 

Practice problem.

 

Problem 1: Convert AB16 into decimal number.

Solution:    171

Problem 2: Convert D316 into decimal number.

Solution:    211

Problem 3: Convert 5216 into decimal number.

Solution:    82



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