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 × 16^{2}) + (12 × 16^{1}) + (15 × 16^{0})
= (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 }… d_{3} d_{2} d_{1} d_{0}
Multiply each digit of the hex number with its corresponding powers of 16 and add them such as:
d_{n-1 }× 16^{n-1} + … + d_{3 }× 16^{3} + d_{2 }× 16^{2} + d_{1} × 16^{1} + d_{0} × 16^{0}
Thus, the resultant number will be taken as base 10 or decimal number system.
d_{n-1 }… d_{3} d_{2} d_{1} d_{0} (hex) = d_{n-1 }× 16^{n-1} + … + d_{3 }× 16^{3} + d_{2 }× 16^{2} + d_{1} × 16^{1} + d_{0} × 16^{0 }(decimal)
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:
Hexadecimal | Decimal (Equivalent Value) |
1 | 1 |
2 | 2 |
3 | 3 |
4 | 4 |
5 | 5 |
6 | 6 |
7 | 7 |
8 | 8 |
9 | 9 |
A | 10 |
B | 11 |
C | 12 |
D | 13 |
E | 14 |
F | 15 |
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.
- Number system
- Hexadecimal to binary conversion
- Hexadecimal to octal conversion
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 × 16^{3}) + (13 × 16^{2}) + (10 × 16^{1}) + (6 × 16^{0})
= (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 × 16^{2}) + (8 × 16^{1}) + (11 × 16^{0})
= (14 × 256) + (8 × 16) + (11 × 1)
= 3584 + 128 + 11
= 3723
Therefore, (E8B)_{16} = (3723)_{10}
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Frequently Asked Questions on Hex to Decimal
Q1
What is a hexadecimal number system?
The hexadecimal number system uses sixteen digits, such as 0,1, 2, 3, 4, 5, 6, 7, 8, 9 and A, B, C, D, E, F with the base as 16.
Q2
What is a decimal number system?
The decimal number system uses ten digits, such as 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 with the base as 10.
Q3
How to convert the hexadecimal number system to the decimal number system?
To convert the hexadecimal number system to the decimal number system, follow the below steps:
Step 1: Multiply each digit with the powers of 16 starting from the units place of the number.
Step 2: Simplify each of the products and add them.
Q4
Convert 7CA (hex) to decimal.
We know that 7 = 7, C = 12 and A = 10.
Therefore (7CA)_{16} = (7 × 16^{2}) + (12 × 16^{1}) + (10 × 16^{0})
(7CA)_{16} = (7 × 256) + (12 × 16) + (10 × 1)
(7CA)_{16} = 1792+192+10
(7CA)_{16} = (1994)_{10}
Hence, 7CA (hex) to decimal is 1994.
Q5
Convert 5BC (hex) to decimal.
We know that 5 = 5, B = 11 and C = 12.
Therefore (5BC)_{16} = (5 × 16^{2}) + (11 × 16^{1}) + (12 × 16^{0})
(5BC)_{16} = (5 × 256) + (11 × 16) + (12 × 1)
(5BC)_{16} = 1280+176+12
(5BC)_{16} = (1468)_{10}
Hence, 5BC (hex) to decimal is 1468.