Hex to Decimal

Hexadecimal number system (also known as base 16) is a positional system that represents numbers using a base 16. Unlike the common ways of representing the numbers using 10 symbols, it uses 16 different symbols to represent numbers. The symbols 0 - 9 represent values zero to nine, where the symbols A to F represent values ten to fifteen. These symbols are used to convert hexadecimal numeral systems to another system using certain rules of conversion. Programmers and Computer System Designers frequently use hexadecimal number systems as they provide a human-friendly representation of binary codes. Here, you will learn about hexadecimal numeral systems and conversion from hex to decimal along with examples.

What is a Hexadecimal Number?

The hexadecimal numeral system (also abbreviated as hex) is the system of numbers which have 16 digits, rather than 10. The standard numeral system is known as the decimal system (base 10) and uses 10 symbols i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The hexadecimal numbers system includes 10 decimal numbers and extra six symbols. There are no numerical symbols that represent the value greater than 9, hence English alphabets such as A, B, C, D, E, and F are used to represent hexadecimal numeral systems.

The 16 digits in the hexadecimal number system are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, where A is 10, B is 11, C is 12, etc.

In the Hexadecimal number system, the place value of a number is determined by the power of 16, rather than 10. For example,

2A316 = 2 * 16² + 10 * 16¹ + 3 * 16º = 67510

Conversion From Hex to Decimal

To convert hex to a decimal manually, you should first start multiplying the hex numbers by 16. Then, you raise it to a power of 0 and increase that power each time by 1 according to the hexadecimal equivalent system.

While applying powers, we will start with the right of a hexadecimal number system and move to the left. Each time you multiply a number by 16, the power of 16 increases.

Let understand the conversion from hex to decimal with an example given below:

Convert (7CF)16 to decimal number.

Solution:

In Hexadecimal number system,

7 = 7

C = 12

F = 15

To convert 7CF into a decimal number, multiply each digit with the power of 16 starting from the unit place of a hexadecimal system.

Accordingly, (7CF)16 can be expressed as:

(7CF)16 =  (7* 16²) +  (12 * 16¹) + (15 * 16⁰)

= (7 * 256) + (12 * 16) + (15 * 1)

= 1792 + 192 + 7

= 19999

Therefore, (7CF)16 = (19999)10

The conversion table for the numbers from hex to decimal is given below:

Hex to Decimal Table

The above-given hex to the decimal table helps you to represent the digits and numbers individually in large numbers in a hexadecimal numeral system.

Solved Examples

Let's look at some examples of conversion from hexadecimal to decimal number systems with detailed explanations.

1. Convert (2C7)16 to decimal number.

Solution:

In Hexadecimal Number System,

2 = 2

C = 12

7 = 7

Hence,

(2C7)16 =  (2 * 16²) +  (12 * 16¹) +  (7 * 16⁰)

= (2 * 256) +  (12 * 16) +  (7 * 1)

= 512 + 192 + 7

= 711

Therefore, (2C7)16 = (711)10

2. Convert (1A7D)16 to decimal number

Solution:

In Hexadecimal Number System,

1 = 1

A = 10

7 = 7

D = 13

Hence,

(1A7D)16 =  (1 * 16³) +  (10 * 16²) +  (7 * 16¹) +  (13 * 16º)

= (1 * 4096) +  (10 * 256) +  (7 * 16) +  (13 * 1)

= 4096 + 2560 + 112 + 13

= 6781

Therefore, (1A7D)16 = (6781)10

Hex to Decimal

The important concept in math is the number system as it is being used for representing the numbers and classifying them on the basis of their base numbers. There are a lot of types of number systems and some of them are named as octal, binary, decimal, hexadecimal and so on. We can very easily convert one base system into another by using some rules of conversion. 

Hexadecimal to Decimal

In the number system, hexadecimal to decimal is the process of conversion of one number into another. The representation of numbers by using the digits or other symbols in a very consistent manner is known as the number system. Each type of number system has its own unique base number which distinguishes between the systems. Hexadecimal has a base number of 16 and the decimal number system has a base number of 10.

Hexadecimal to Decimal Conversion

Hexadecimal to decimal conversion is being done by keeping in mind the base numbers of each of the number systems. The operation of the hexadecimal number system is with both the digits and characters, especially for the representation of the double digit characters which are being used. In total, there are 16 notations in this and they are - 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 and 10 to 15 is being represented as A, B, C, D, E and F. Whereas in the system of decimal number, 10 notations are being represented as 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. For converting the hexadecimal to decimal, firstly we have to obtain the decimal which is equivalent to hexadecimal from the conversion table, multiply as digit with 16 to the power of the location of digit and add up all together. 

How to Convert Hexadecimal to Decimal

For converting the hexadecimal to a decimal we have to use the base number 16 for its conversion. The digit of the hexadecimal is being expanded to multiply each of its digits which have the power of 16. The power starts at 0 from the right and moves forward towards the right with the increase in power. For making this process of conversion to complete, the multiplied numbers are then added.

Formula for Converting Hexadecimal to Decimal

There is a formula which is being used for converting the hexadecimal to decimal and it is explained below-

Firstly, the base of the number has to be converted, which is 16 here. Then we need to multiply each digit of the number which was given, starting from the rightmost digit which was with the exponents of the base 16. Here the exponents must be started from 0 and every time it should be increased by 1 as we will move from right to left. Then simply, we just have to take each of the products and add them.