How to Convert Hex to Decimal

Hexadecimal to Decimal

Hexadecimal to decimal is the process of converting one number from hexadecimal system to decimal system. Hexadecimal has a base number of 16 whereas the decimal number system has a base number of 10.

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. Let us learn how to convert hex to decimal, the conversion table, and solve a few examples to understand the concept better.

What is Hexadecimal to Decimal Conversion?

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 characters are used to represent double-digit numbers. There are a total of 16 notations in hexadecimal system: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 and 10-15 is represented by the letters A-F respectively. 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 digit equivalent of hexadecimal from the conversion table, multiply the digits with 16 to the power of digit location (we start from right most digit and move to the left by multiplying the digits by 16⁰, 16¹, 16², ...) and add them 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 next digit. Hence, when we convert any hexadecimal number to decimal 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.

How to Convert Hexadecimal to Decimal?

The conversion of hexadecimal to decimal is done by using the base number 16. To convert a number from hexadecimal to decimal form:

• Step 1: Write the decimal equivalent of each digit of the number in hexadecimal form (from the above table)
• Step 2: Multiply the digits from right to left with exponents of 16⁰, 16¹, 16², ... in order starting from the right most digit.
• Step 3: Then add all the products. The resultant sum is the number in the decimal system.

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.

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

Where,

• n = the number of digits.
• r = placement of the digit (from the right side starting from r = 0)

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.

☛Also Check: HEX to Decimal Converter

Hexadecimal to Decimal Formula

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 … d₁ d₀ (hex) = d_n-1 × 16^n-1 + … + d₁ × 16¹ + d₀ × 16⁰ (decimal)

Hexadecimal to Decimal Examples

Example : Convert (5BC)₁₆ into the decimal system.

Solution:

To find: (5BC)₁₆ in the decimal system

In Hexadecimal system,

5 = 5

B = 11

C = 12

Using hexadecimal to decimal formula,

(5BC)₁₆ = ( 5 × 16² + 11 × 16¹ + 12 × 16⁰ )

= 5 × 256 + 11 × 16 + 12× 1

= (1468)₁₀

Answer: Therefore, (5BC)₁₆ =(1468)₁₀