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.

How to Convert Hexadecimal to Decimal

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

Decimal Number = d_n-1 × 16^r-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.

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.