The number system is an important concept in maths as it is used to represent the numbers and classify them based on their base numbers. There are various types of number systems namely binary, octal, decimal, hexadecimal and so on. We can easily convert one base system to another using certain rules of conversion. In this article, you will learn about hexadecimal and decimal systems, conversion from hex to decimal, table, conversion procedure along with examples.

Table of Contents:

• Hexadecimal Number System
• Decimal Number System
• Hex to Decimal Conversion
• Converter
• Table
• Examples
• FAQs

Hexadecimal Number System

The base of a hexadecimal system is 16. The 16 symbols involved in this system include 10 decimal digits and the first six letters of the English alphabet, i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. Here, the alphabets can be treated 10, 11, 12, 13, 14 and 15, respectively. Learn more about the hexadecimal system here.

Decimal Number System

A number system that uses digits from 0 to 9 to represent a number with base 10 is called the decimal number system. The number is expressed in base-10, where each value is denoted by 0 or the first nine positive integers. Each value in this number system has the place value of power 10. It means the digit at the tens place is ten times greater than the digit at the unit place.

Conversion from Hex to Decimal

As we know, number systems can be converted from one base to another. Thus, we can convert hexadecimal numbers to decimal easily. This number system conversion can be done as explained in the example given below:

Example:

Convert 7CF (hex) to decimal.

Solution:

Given hexadecimal number is 7CF.

In hexadecimal system,

7 = 7

C = 12

F = 15

To convert this into a decimal number system, multiply each digit with the powers of 16 starting from units place of the number.

7CF = (7 × 16²) + (12 × 16¹) + (15 × 16⁰)

= (7 × 256) + (12 × 16) + (15 × 1)

= 1792 + 192 + 15

= 1999

From this, the rule can be defined for the conversion from hex numbers to decimal numbers.

Suppose below is the hex number with n digits:

d_n-1 … d₃ d₂ d₁ d₀

Multiply each digit of the hex number with its corresponding powers of 16 and add them such as:

d_n-1 × 16^n-1 + … + d₃ × 16³ + d₂ × 16² + d₁ × 16¹ + d₀ × 16⁰

Thus, the resultant number will be taken as base 10 or decimal number system.

Hex to Decimal Converter

There is a tool available to convert the numbers from hexadecimal to decimal number system.

Click here for a quick hexadecimal conversion to decimal.

Hex to Decimal Table

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

This table will help in representing the digits and letters individually in the large numbers in base 16 system as explained above.

Also, learn about decimal to hex conversion here.

Solved Examples

Let us have a look at the examples of conversion of numbers from hexadecimal (base 16) to the base 10 number system, with detailed explanations.

Example 1:

Convert (1DA6)₁₆ to decimal.

Solution:

(1DA6)₁₆

Here,

1 = 1

D = 13

A = 10

6 = 6

Thus,

(1DA6)₁₆ = (1 × 16³) + (13 × 16²) + (10 × 16¹) + (6 × 16⁰)

= (1 × 4096) + (13 × 256) + (10 × 16) + (6 × 1)

= 4096 + 3328 + 160 + 6

= 7590

Therefore, (1DA6)₁₆ = (7590)₁₀

Example 2:

Convert (E8B)₁₆ to decimal system.

Solution:

(E8B)₁₆

Here,

E = 14

8 = 8

B = 11

Thus,

(E8B)₁₆ = (14 × 16²) + (8 × 16¹) + (11 × 16⁰)

= (14 × 256) + (8 × 16) + (11 × 1)

= 3584 + 128 + 11

= 3723

Therefore, (E8B)₁₆ = (3723)₁₀

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