Hexadecimal to Decimal Conversion – Steps, Chart, Facts, Examples

What Is the Hexadecimal to Decimal Conversion?

The hexadecimal to decimal conversion is used to convert numbers from the base-16 number system to base-10 number system. 

What Is the Hexadecimal Number System?

The base of a hexadecimal number system is 16. It uses the 16 symbols given by 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F to write all the numbers. The place values in the hexadecimal number system are defined in terms of powers of 16. 

What Is the Decimal Number System?

Decimal number system is a base-10 number system that uses digits from 0 to 9 for representing a number with base 10. The place values are defined in terms of powers of 10.

Hexadecimal to Decimal Chart

The decimal values for the digits 0 to 9 remain the same, while the letters A to F represent decimal values 10 to 15, respectively. This table is helpful in converting hexadecimal numbers to decimal.

Hexadecimal	Decimal (Equivalent Value)
0	0
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

How to Convert Hexadecimal to Decimal

Step 1: Assign decimal values to each hexadecimal digit using the table given. The decimal values for the digits 0 to 9 remain the same, while the letters A to F represent decimal values 10 to 15, respectively.

Step 2: Starting from the rightmost digit, multiply each digit by the corresponding power of 16 (16 raised to the power of its position). The rightmost digit has a position of 0, the next digit to the left has a position of 1, and so on.

Step 3: Sum up the products obtained in step 2 to get the decimal equivalent.

Hexadecimal to Decimal Conversion Examples 

Let’s discuss a few examples to understand the steps we discussed in the previous section.

Example 1: Convert $(36)_{16}$ into decimal form. 

$(3 \times 6)_{16} = (3 \times 16^{1}) + (6 \times 16^{0})$

$(36)_{16} = 3 \times 16 + 6$

$(36)_{16} = 48 + 6$

So, $(36)_{16} = (54)_{10}$

Example 2: $(2A5D)_{16}$

In this example, we will first obtain the decimal equivalent for the symbol A and D from the conversion table given below. 

A = 10, D = 13

Thus, $(2A5D)_{16} = (2 \times 16^{3})+(10 \times 16^{2}) + (5 \times 16^{1}) + (13 \times 16^{0})$

$(2A5D)_{16} = (2 \times 4096) + (10 \times 256) + (5 \times 16) + (13 \times 1)$

$(2A5D)_{16} = (10845)_{10}$

Facts about Hexadecimal to Decimal Conversion

Conclusion

In this article, we learned about hexadecimal to decimal conversion. Understanding this conversion allows us to work with hexadecimal numbers more efficiently. Let’s reinforce our knowledge with practice examples and MCQs for better comprehension. Happy converting!

Solved Examples on Hexadecimal to Decimal Conversion

1. Convert (4B6)₁₆ into a decimal system.

Solution: 

In the Hexadecimal system,

4 = 4, B = 11 and 6 = 6

$(4B6)_{16} = (1 \times 16^{2})+(13 \times 16^{1}) + (9 \times 16^{0})$

$(4B6)_{16} = 196 + 208 + 9$

$(4B6)_{16} = = (413)_{10}$

2. What is the value of $(5D)_{16}$ into a decimal system?

Solution: 

5 = 5 and D = 13

$(5D)_{16} = (5 \times 16^{1}) + (13 \times 16^{0})$

$(5D)_{16} =80 + 3$

$(5D)_{16} = (83)_{10}$

3. Convert $(FA9)_{16}$ into a decimal system.

Solution: 

F = 15, A = 10 and 9 = 9

$(FA9)_{16} = (15\times 16^{2}) + (10 \times 16^{1}) + (9 \times 16^{0})$

$(FA9)_{16} = 15 \times 256 + 10 \times 16 + 9$

$(FA9)_{16} = 3840 + 160 + 9$

$(FA9)_{16} = (4009)_{10}$

4. What is the value of $1B8E_{16}$ in the decimal system? 

Solution: 

1 = 1, B = 11 , 8 = 8 and E = 14

$(1B8E)_{16} = (1 \times 16^{3}) + (11 \times 16^{2}) + (8 \times 16^{1}) + (14 \times 16^{0})$

$(1B8E)_{16} = 1 \times 4096 + 11 \times 196 + 8 \times 16 + 14$

$(1B8E)_{16} = 4096 + 2156 + 128 + 14$

$(1B8E)_{16} = (6394)_{10}$

5. Convert $5CD81_{6}$ in the decimal system.

Solution: 

5 = 5, C = 12, D = 13, and 8 = 8

$(5CD8)_{16} = (5 \times 16^{3}) + (12 \times 16^{2}) + (13 \times 16^{1}) + (8 \times 16^{0})$

$(5CD8)_{16} = 5 \times 4096 + 12 \times 196 + 13 \times 16 + 8$

$(5CD8)_{16} =20,480 + 2,352 + 208 + 8$

$(5CD8)_{16} =(23048)_{10}$

Practice Problems on Hexadecimal to Decimal Conversion

Frequently Asked Questions on Hexadecimal to Decimal Conversion