Hex to Decimal: Formula, Conversion and Table

Hexadecimal to decimal is a process of converting one number of a hexadecimal number system to another in a decimal number system. Representation of numbers continually using digits or other symbols is known as the number system. There is a total of four types of number systems: binary, octal, decimal, and hexadecimal. 

Each of these number systems has its unique base number that distinguishes between the systems. 

Also Read: Decimal Expansion of Rational Numbers

Key Terms: Number system, Hexadecimal, Decimal, Octal, Binary, Digits, Power

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Hexadecimal Number System

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The number system with 16 as its base or where each digit weights power 16, is the hexadecimal number system. In this number system, each digit is 16 times more powerful than the last one.

There are a total of 16 symbols involved in this system of which ten are digits while the rest six are alphabets. The symbols are given as follows.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

Here, A, B, C, D, E, F are considered to be as equivalent to 11, 12, 13, 14, 15, and 16 respectively.

Also Read:

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Decimal Number System

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The number system that has 10 as its base or the system where each digit has a place value of power 10, is the decimal number system. In this number system, the digit at the tens places is 10 times greater than the digit at the unit place. 

The decimal system has 10 symbols and all of them are digits ranging from 0 to 9. The decimal number system is given below. 

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Also Read: Binary Operations

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Conversion Hex to Decimal

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Hexadecimal can be converted to decimals by using the base number 16. The conversion takes place in the following steps.

• Find the decimal equivalent of hexadecimal from the conversion table.
• Multiply each digit with the power of 16 starting at 0 from the right.
• Add all the numbers together for conversion to complete.

The hexadecimal table is given below for easy conversion.

The Conversion Table

Let us take an example for better understanding.

Example: Convert (20)₁₆ to its decimal equivalent.

Solution: Here, following the above-mentioned steps

(20)₁₆ = 2 x 16¹ + 0 x 16⁰

(20)₁₆ = 32 + 0 = 32

(20)₁₆ = (32)₁₀

Also Read: Exponents

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Hex to Decimal Formula

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The formula to convert hexadecimal to decimal is given below.

d_n-1….d₁d₀(Hexadecimal) = d_n-1 x 16 ^n-1+..…+ d₁ x 16¹ + d₀ x 16⁰(Decimal)

Let us take an example to understand better.

Example: Convert (12)₁₆ to its decimal form.

Solution: Using the above-mentioned formula

(12)₁₆ = 1 x 16¹ + 2 x 16⁰ = 16 + 2 = (18)₁₀

Also Read: Greatest Integer Function

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Hex to Decimal Table

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Hexadecimal to decimal conversion table is given below:

Also Read: Arithmetic Operations

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Things to Remember

• Hexadecimal number system has 16 as its base.
• Decimal number system has 10 as base and each digit has a place value of power 10.
• The hexadecimal number system has 16 symbols where 9 are digits while 6 are alphabets.
• The formula to convert hexadecimal to decimal is 

d_n-1….d₁d₀(Hexadecimal) = d_n-1 x 16 ^n-1+..…+ d₁ x 16¹ + d₀ x 16⁰(Decimal)