“Hex to Decimal” is an article on the concept of converting numerals from one number system to another, specifically from the Hexadecimal Number System to the Decimal Number System. As we know, a number system is used to represent and categorize numbers based on their base numbers, which is a fundamental concept in mathematics.
When converting from hexadecimal to decimal, it is important to keep consideration for both number system’s base. The hexadecimal numeral system, usually known as base-16 or just “hex,” is a system of positional digits that uses the base of 16 to represent numbers in mathematics and computing. Hexadecimal employs sixteen different symbols as opposed to the decimal system’s ten, which are “0” through “9” for 0 to 9 and “A” through “F”for ten to fifteen.
This article provides a well-rounded description of the Hexadecimal Number System, the Decimal Number System, and how to convert hexadecimal numerals into decimal numerals.
Table of Content
- What is Hexadecimal Number System?
- What is Decimal Number System?
- Hex to Decimal Formula
- How to Change Hexadecimal to Decimal?
- Hex to Decimal Conversion Table
What is Hexadecimal Number System?
The hexadecimal number system, commonly known as base-16 or just hex, is a system of numbers that employs 16 different symbols for representing various values. There are only 16 symbols used for denoting hexadecimal integers. A, B, C, D, E, and F are the following values or symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. A decimal value is represented by each digit. D, for instance, is equal to base-10 number 13. This table, which lists the 16 hexadecimal digits and their decimal, octal, and binary equivalents, will be useful for converting between number systems. The following list is additionally useful as a converter or translator.
Numerals in Hexadecimal Number System
This number system uses 16 different symbols.
Numeral | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Used For | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
Example of Hexadecimal Numbers
As hexadecimal is a number system, all numbers in decimal and other number systems can also be represented in the hexadecimal number system. The following table represents some numbers in hexadecimal, decimal, octal, and binary as well.
Hexadecimal (Base 16) | Decimal (Base 10) | Octal (Base 8) | Binary (Base 2) |
---|---|---|---|
1A3F | 6719 | 15177 | 1101000111111 |
FF | 255 | 377 | 11111111 |
2E | 46 | 56 | 101110 |
10 | 16 | 20 | 10000 |
A0B | 2571 | 5003 | 101000001011 |
7F | 127 | 177 | 1111111 |
3D4 | 980 | 1714 | 1111010100 |
5C6 | 1478 | 2666 | 10111000110 |
FFF | 4095 | 7777 | 111111111111 |
1000 | 4096 | 10000 | 1000000000000 |
What is Decimal Number System?
Any number with a decimal point in between the full amount and the fractional portion is said to be decimal. These two components of the decimal are separated by the point. It is known as a decimal point as a result. The figures following the decimal point always remain less than one.
Numerals in Decimal Number System
There are 10 numerals in decimal number system as it has base of 10. These numerals are:
Numeral | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|
Parts of Decimal Numbers
For any number in the decimal system, there are two components i.e., Whole Part and Decimal Part.
- Whole Number Part: The component of the whole number is made up of the digits to the left of the decimal point. The locations start with ones, then go through ones, tens, hundreds, thousands, and furthermore.
- Decimal Part: The decimal point and the digits to its right make up the fractional component of the decimal part, which is why it is never greater than 1. Tenths are used as the starting point, followed by hundredths, thousandths, and so forth.
Example of Decimal Numbers
The decimal numbers are 13.168 and 4.681 where 13 and 4 are whole numbers, whereas 168 and 681 are decimal points. The decimal number’s fractional component is less than 1. Some other examples are:
- 12
- 345
- 6.75 (Decimal Fractions)
- -123 (Negative Decimal Number)
- 1000 (Large Positive Decimal Number)
Hex to Decimal Formula
For the conversion to be complete, the multiple numbers must be added. The hexadecimal digit is expanded to multiply each digit with the power of 16, starting at 0 from the right and moving forward towards the right with the increase in power.
Decimal Number = d_{n-1 }× 16^{r-1}+ d_{n-2} × 16_{r-2} . . . + d_{2} × 16^{2} + d_{1} × 16^{1} + d_{0} × 16^{0}
Where,
- n is the number of digits, and
- r is the placement of the digit (from the right side starting from r = 0), and
- d id the decimal value of the corresponding digit.
Let’s consider an example to better understand the use of this formula.
Example: Covert 1A3 into decimal numbers.
Solution:
Start from the rightmost digit i.e., 3. Its position is 0.
Decimal Value = 3 × 16^{0} = 3 × 1 = 3
Move to the next digit i.e., A with a position of 1.
Since A represents 10 in decimal, the calculation becomes:
Decimal Value = 10 × 16^{1} = 10 × 16 = 160
Finally, move to the leftmost digit i.e., 1 with a position of 2.
Decimal Value = 1 × 16^{2} = 1 × 256 = 256
Thus, Decimal Value of 1A3 = 3 + 160 + 256 = 419
So, the hexadecimal number “1A3” is equivalent to the decimal number 419.
How to Change Hexadecimal to Decimal?
Using the base number 16, hexadecimal to decimal conversion is performed. From hexadecimal to decimal conversion of a number:
Step 1: From the table previously mentioned, write the number’s hexadecimal equivalent in decimal form for each digit.
Step 2: Beginning with the rightmost digit, multiply the digits in order from right to left with exponents of 16 i.e., 16^{0}, 16^{1}, 16^{2}, . . .
Step 3: Following that, add each product. The decimal number is the sum of the results.
Example of Hex to Decimal Conversions
Number systems can be changed from one base to another, as is well known. As a result, it is simple to alter hexadecimal values to decimal. This number system conversion can be carried out as demonstrated in the following example:
Example: Convert 6CF (hex) to decimal.
Solution:
6CF is the given hexadecimal number. In hexadecimal number system
- 6 = 6
- C = 12
- F = 15
Start at the unit’s place of the number and multiply each digit by a power of 16 in order to convert this to a decimal number system.
6CF= (6 × 16^{2}) + (12× 16^{1}) + (15 × 16^{0})
⇒ 6CF= (6 × 256 + 12 × 16 + 15 × 1)
⇒ 6CF= 1536 + 192 + 15
See AlsoHow to Convert Hexadecimal to Binary or Decimal: 6 StepsHex to Decimal (Table, Formula & Conversion)Hexadecimal to Decimal ConverterHexadecimal to Decimal - Conversion, Formula | How to Convert?⇒ 6CF= 1743
Thus, decimal value of 6CF is 1743.
Read More about Decimal to Hexadecimal Converter.
Hex to Decimal Conversion Table
Hex to Decimal Conversion Table is a lookup table for hexadecimal numerals where we can see the value of each numeral in the decimal number system. Hex to Decimal conversion table for the 16 hexadecimal digits is given as follows:
Hexadecimal | Decimal |
---|---|
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 |
You can use this table to convert hexadecimal digits to their decimal equivalents. For example, if you have the hexadecimal digit “A,” you can look it up in the table to find that it is equivalent to the decimal number 10.
Read More,
- Binary to Decimal Converter
- Binary to Hexadecimal Converter
Solved Problems on Hex to Decimal
Problem 1: Convert 31.D2_{16.}
Solution
As we know,
Digit 3 1 D 2 Place value 16^{1} 16^{0} 16^{-1} 16^{-2} 31.D2_{16 }= (3×16^{1}) + (1×16^{0}) + (D×16^{-1}) + (2×16^{-2})
⇒ 31.D2_{16 }= 48 + 1 + 13×16^{-1} + 2×16^{-2}
⇒ 31.D2_{16 }= 48 + 1 + 0.8125 + 0.0078125
⇒ 31.D2_{16 }= 49.8203125
Problem 2: Convert (4C7) to a decimal number.
Solution:
In Hexadecimal Number System,
4= 4, C = 12, and 7 = 7
Hence, (4C7)_{16} = (4× 16²) + (12 × 16¹) + (7 × 16⁰)
⇒ (4C7)_{16 }= (4 × 256) + (12 × 16) + (7 × 1)
⇒ (4C7)_{16 }= 1024 + 192 + 7
⇒ (4C7)_{16 }= 1223
Therefore, (2C7)_{16 }= (1223)_{10}
Problem 3. Convert (16F) into its equivalent Decimal number.
Solution:
We have a hexadecimal number 16F that we want to convert into a decimal number.
We know that 1 = 1, 6 = 6 and F = 16.
Therefore (16F)_{16} = (1 × 16^{2}) + (6 × 16^{1}) + (16 × 16^{0})
⇒ (16F)_{16} = (1 × 256) + (6 × 16) + (16 × 1)
⇒ (16F)_{16} = 256 + 96 + 16
⇒ (16F)_{16} = (368)_{10}
Hence, (16F)_{16} to decimal is 368.
Problem 4. Convert 5BC (hex) to decimal.
Solution:
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)_{16} is 1468 in decimal number system.
Problem 5. Convert (5EC)_{16} to decimal.
Solution:
As we know,
In hexadecimal system, E = 14,
∴ (5EC)_{16} = (5 × 16²) + (14 × 16¹) + (12 × 16⁰) = 1696
Hence, (5EC)_{16} = (1696)_{10}
Problem 6. Convert 4CD from Hexadecimal to Decimal.
Solution:
We know that 4 = 4, C = 12, and D = 13 in hexadecimal (hex).
Therefore, to convert the hexadecimal number 4CD to decimal, we can use the positional notation method:
(4CD)₁₆ = (4 × 16²) + (12 × 16¹) + (13 × 16⁰)
⇒ (4CD)₁₆ = (4 × 256) + (12 × 16) + (13 × 1)
⇒ (4CD)₁₆ = 1024 + 192 + 13
⇒ (4CD)₁₆ = (1229)₁₀
Hence, 4CD (hex) to decimal is 1229.
Problem 7. Convert 1AB from Hexadecimal to Decimal.
Solution:
We know that 1 = 1, A = 10, and B = 11 in hexadecimal (hex).
Therefore, to convert the hexadecimal number 1AB to decimal, we can use the positional notation method:
(1AB)₁₆ = (1 × 16²) + (10 × 16¹) + (11 × 16⁰)
⇒ (1AB)₁₆ = (1 × 256) + (10 × 16) + (11 × 1)
⇒ (1AB)₁₆ = 256 + 160 + 11
⇒ (1AB)₁₆ = (427)₁₀
Hence, 1AB (hex) to decimal is 427.
Problem 8. Convert 5BC (hex) to decimal.
Solution:
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.
Problem 9. Convert 1D9 (hexadecimal) to decimal.
Solution:
In the Hexadecimal system,
1 = 1, D = 13, and 9 = 9
(1D9)_{16}= (1 × 16^{2} + 13 × 16^{1} + 9 × 16^{0} )
⇒ (1D9)_{16} = 1 × 256 + 13 × 16 + 9 × 1
⇒ (1D9)_{16 }= (473)_{10}
Practice Problems on Hex to Decimal
Problem 1: Convert the hexadecimal number “1A” to decimal.
Problem 2: Change hexadecimal to decimal for the value “2F.”
Problem 3: Converting hexadecimal to decimal, what is the decimal representation of “7B”?
Problem 4: Use a hexadecimal to decimal converter to find the decimal equivalent of “3D8.”
Problem 5: How to change hex to decimal for the hexadecimal number “FFFF”?
Problem 6: How do you convert hex to decimal for the value “4A5”?
Problem 7: From hex to decimal, calculate the decimal value of “B2E” in hexadecimal.
Problem 8: Hex to decimal: Find the decimal value of “5C.”
Problem 9: What is the process of converting “1E4” from hexadecimal to decimal?
Problem 10: Convert the value “AA” from hexadecimal to decimal and then to binary.
Hex to Decimal Conversion – FAQs
1. 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.
2. 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.
3. 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 unit’s place of the number.
- Step 2: Simplify each of the products and add them.
4. Can Hexadecimal Numbers Represent Fractions?
Yes, fractions can be represented by hexadecimal numbers. However, it is not simple to change a decimal fraction into a hexadecimal fraction. One method for doing this is to convert the integer portion of the fraction to hexadecimal after multiplying the decimal portion by an even number of hex digits.
5. Is There a Shortcut to Convert Hex to Decimal?
Yes, there are shortcuts and methods to convert hexadecimal (hex) numbers to decimal without manually converting each digit. One of the most common shortcuts is to use the following steps:
- Write down the hexadecimal number.
- Assign decimal values to each hex digit (0-9 remain the same, and A=10, B=11, C=12, D=13, E=14, F=15).
- Start from the rightmost digit (the least significant digit).
- Multiply the value of the digit by 16 raised to the power of its position (starting from 0 for the rightmost digit).
- Add up all these products to get the decimal equivalent.
6. How do I Convert Hexadecimal to Decimal?
Using the base number 16, hexadecimal to decimal conversion is performed. From hexadecimal to decimal conversion of a number:
- Step 1: From the table previously mentioned, write the number’s hexadecimal equivalent in decimal form for each digit.
- Step 2: Beginning with the rightmost digit, multiply the digits in order from right to left with exponents of 16 i.e., 160, 161, 162, . . .
- Step 3: Following that, add each product. The decimal number is the sum of the results.
7. What is Hexadecimal (Hex)?
The hexadecimal number system, commonly known as base-16 or just hex, is a system of numbers that employs 16 different symbols to represent various values. These are the 0–9 and A–F symbols.
8. Can I Convert Negative Hexadecimal Numbers to Decimal?
Negative hexadecimal values can be converted to decimal. Converting positive hexadecimal values to decimal with this method is comparable.
9. What is Hex to Decimal Converter?
A hexadecimal to decimal converter is a program that converts hexadecimal numbers to decimal equivalents. In other terms, it converts a number in base-16 (hexadecimal) to base-10 (decimal).
10. What is Hex to Decimal Formula?
Decimal Number = d_{n-1} × 16^{r-1}+ d_{n-2 }× 16^{r-2} . . . + d_{2 }× 16^{2} + d_{1 }× 16^{1 }+ d_{0} × 16^{0}
Where,
- n is the number of digits,
- r is the placement of the digit (from the right side starting from r = 0), and
- d is the decimal value of the corresponding digit.
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