Last modified on August 3rd, 2023

chapter outline

 

Hexadecimal to Decimal

Hexadecimal (hex in short) to decimal is the process of converting hexadecimal numbers to decimal numbers. The hexadecimal number system is generally used to express larger numbers with fewer digits.

Hexadecimal number system consists of numbers with the base of 16. It has 16 notations starting from 0 to 15, where 10 to 15 are expressed with alphabets A to F.

In contrast, the decimal number system consists of numbers with the base of 10.  It has 10 notations, starting from 0 to 9.

The table below represents the relation between the hexadecimal numbers with the decimal numbers.

Hexadecimal0123456789ABCDEF
Decimal0123456789101112131415

How to Convert Hexadecimal to Decimal

Here, we will be using the same formula to convert a decimal to hexadecimal.

Decimal Number = dn-1 × 16r-1+….+ d2 × 162 + d1 × 161 + d0 × 160

Here, n = number of digits, r = place of the digit

Now we will learn how to convert a hexadecimal number to a decimal number as shown in the example below.

Hexadecimal to Decimal

Following the above example, let us solve some more examples.

Solved Examples

Convert (7EC)16 to decimal.

Solution:

As we know,
In hexadecimal system, E = 14,
∴ (7EC)16 = (7 × 16²) + (14 × 16¹) + (12 × 16⁰) = 2028
Hence, (7EC)16 = (2028)10

Express (2A1ED)16 to decimal.

Solution:

As we know,
In hexadecimal system, A = 10, E = 14, D = 13
(2A1ED) 16 = (2 × 16⁴) + (10 × 16³) + (1 × 16²) + (14 × 16¹) + (13 × 16⁰) = (172525) 10

Conversion Table

A reference chart is shown below which can help us to convert hexadecimal to decimal or other numbers like binary.

Hex to Decimal Table

Last modified on August 3rd, 2023

Leave a comment

Your email address will not be published. Required fields are marked *