Hexadecimal to Decimal

Hexadecimal to decimal is the process of converting one number to another in a number system. A number system is a representation of numbers by using digits or other symbols in a consistent manner. There are four types of number systems namely, binary, octal, decimal, and hexadecimal. Each of these has its own unique base number that distinguishes between the systems. Hexadecimal has a base number of 16 whereas the decimal number system has a base number of 10. Let us learn how to convert hexadecimal to decimal, the conversion table, and solve a few examples to understand the concept better.

Hexadecimal to decimal conversion is done by keeping the base numbers of each of the number systems in mind. The hexadecimal number system operates with both digits and characters especially to represent the double-digit, characters are used. There are a total of 16 notations: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 and 10-15 is represented as A, B, C, D, E, F. Whereas in the decimal number system, 10 notations are represented as 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. To convert hexadecimal to decimal, we first obtain the decimal equivalent of hexadecimal from the conversion table, multiply as digit with 16 to the power of digit location and add all together. The conversion table is mentioned below:

Hexadecimal Number System Definition

A hexadecimal number system is also known as a positional number system as each digit has a weight of power 16. Each digit is 16 times more significant than the previous digit. Hence, when we convert any hexadecimal number to any other number system, we multiply the digits individually keeping the power of 16 in mind according to the placement of their position. This number system uses sixteen digits/alphabets: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and A, B, C, D, E, F with the base number as 16. For example, 7DE₁₆, E5F₁₆, 9B4A₁₆.

Decimal Number System Definition

Decimal number system has a base of 10 with digits from 0-9. Numbers in daily life are generally represented in this form. For example, 24₁₀, 654₁₀, 2012₁₀.

The conversion of hexadecimal to decimal is done by using the base number 16. The hexadecimal digit is expanded to multiply each digit with the power of 16. The power starts at 0 from the right moving forward towards the right with the increase in power. For the conversion to complete, the multiplied numbers are added.

Deimal Number = d_n-1 × 16^r-1+....+ d₂ × 16² + d₁ × 16¹ + d₀ × 16⁰.

Where,

• n = number of digits.
• r = placement of the digit.

The steps to convert hexadecimal to decimal are:

• Obtain the decimal equivalent of hexadecimal from the conversion table. (table mentioned above)
• Multiply each digit with the power of 16 starting at 0 from the right.
• Add all the numbers together.

Let us look at an example to understand this better.

For example: Convert hexadecimal number \((25)_{16}\) to its decimal form.

\((25)_{16}\) = 2 × 16¹ + 5 × 16⁰

= 2 × 16 + 5 × 1

= 32 + 5

= 37

Therefore, \((25)_{16}\) = \((37)_{10}\).

Hexadecimal to decimal formula conversion uses the following method:

• The base of the number to be converted here is 16.
• Multiply each digit of the given number, starting from the rightmost digit, with the exponents of the base 16.
• The exponents should start with 0 and increase by 1 every time as we move from right to left.
• We just simplify each of the products and add them.

The hex to decimal conversion formula is given as:

\(d_{n-1} … d_1 d_0 (hex) = d_{n-1} × 16^{n-1} + … + d_1 × 16_1 + d_0 × 16^0 \text{(decimal)}\)

☛Related Topics

Listed below are a few interesting topics related to hexadecimal to decimal, take a look.

• Hexadecimal to Binary
• Decimal to Octal
• Octal to Decimal
• Decimal to Hexadecimal
• Binary to Hexadecimal

What is Meant by Hexadecimal to Decimal?

Hexadecimal to decimal conversion is done by keeping the base numbers of both the number systems in mind. While converting hexadecimal to decimal, the base number 16 is used. The hexadecimal number system uses 16 digits/alphabets: The digits 0,1, 2, 3, 4, 5, 6, 7, 8, 9 and the characters A, B, C, D, E, F, thus having base 16. The decimal number system uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, and thus has base 10.

How to Convert Hexadecimal to Decimal?

Converting hexadecimal to decimal is done by using the base number 16. The steps are as follows:

• Obtain the decimal equivalent of the hexadecimal characters by referring to the conversion table.
• Expand the digits to multiply each digit with the power of 16 that starts 0 from the right to left.
• After the process of multiplication is completed, find the sum.
• The final answer is the decimal number.

What is the Hexadecimal to Decimal Formula?

The conversion formula for hexadecimal to decimal is:

\(d_{n-1} … d_3 d_2 d_1 d_0 (hex) = d_{n-1} × 16^{n-1} + … + d3 × 16^3 + d_2 × 16_2 + d_1 × 16_1 + d_0 × 16^0 \text{(decimal)}\).

How to Use the Hexadecimal to Decimal Formula?

The hexadecimal to decimal formula helps in converting a number given in base 16 to base 10. The formula is used in this method:

• Change the characters to digits by using the conversion table if necessary.
• Multiply each digit of the given number, starting from the rightmost digit, with the exponents of the base 16.
• The exponents should start with 0 and increase by 1 every time as we move from right to left.
• We just simplify each of the products and add them.

What are the Four Types of Number System?

In mathematics, there are four types of number systems, they are:

• Binary number system - The base number is 2
• Octal number system - The base number is 8
• Decimal number system - The base number is 10
• Hexadecimal number system - The base number is 16