Hexadecimal to Decimal

We use decimal numbers from 0 to 9 is used in mathematics. When it comes to the digital system, binary numbers system is used which has only 0 and 1. Therefore, some of the numbers are also used in this number system such as octal and hexadecimal that can be used in digital systems.  A decimal number has a base of 10, binary number has a base of 2, an octal number has a base of 8 and the hexadecimal number has a base of 16.

The hexadecimal number is a way that represents the number which base is 16.

Here, we are going to convert a number in base 16 that is an equivalent number in base 10. This can be used in the digital electronic system where the hexadecimal number can be converted to the decimal number.


Hexadecimal system

A number which consists of base 16 is called as hexadecimal numbers. However, it uses the digits from 0 to 9 when it comes to alphabets it takes from A to F. Therefore, it is the combination of numbers and alphabets. As per, the decimal system and hexadecimal you can have both the numbers from 0 to 9 and remaining numbers from 10 to 15 which represents by alphabets A to F.

10 – A, 11 – B, 12 – C, 13 – D, 14 – E, 15 – F

A hexadecimal number A67 = 10×162+6×161+7×160.

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

Decimal System

Number whose base is 10 is called as decimal numbers. Therefore, decimal numbers include digits from 0 to 9. The decimal number system is the basic number system which can be used widely in everyday mathematics.  However, decimal numbers are used in mathematics but when it comes to digital systems the binary, octal and hexadecimal systems are used here. So, it is very important to know about the conversion of decimal system to this system and vice versa.

Examples: 1) 25 2) 984 4) 21.

How to convert Hexadecimal to Decimal

Some of the steps that convert hexadecimal to decimal are given below

Step 1: Firstly, we have to find the number of hexadecimal digits in the number. There may be n numbers.

Step 2:

You need to multiply each hexadecimal digit with 16n-1, when n is equal to a number of position from the right side.

Step 3:

Later, you have to add each number after multiplication.

Step 4:

The resultant is an equivalent hexadecimal number of the given decimal number.

Converting Hexadecimal to Decimal Examples

Convert 7B16 into decimal number

Given hexadecimal number is 7B 16

7B16 = 161 × 7 + 160 × B

= 16 × 7 + 1 × B

= 112 + 1 × 11

= 112 + 11

= 123

Answer is 123.