Decimal number:

105

(69)16 = (105)10

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Converting hexadecimal numbers to decimal involves multiplying each digit of the hex number by its corresponding power of 16 and then summing the products.

The steps involved are simple and can be easily executed with the help of the following guide.

Conversion Steps

For a hex number with n digits:

dn-1 … d3 d2 d1 d0

The decimal equivalent of the hex number can be obtained by the following formula:

decimal = dn-1×16n-1 + … + d3×163 + d2×162 + d1×161+d0×160

To convert a hex number to decimal, follow these steps:

1. Write down the hex number.
2. Assign each hex digit its corresponding power of 16.
3. Multiply each hex digit by its corresponding power of 16.
4. Sum the products to obtain the decimal equivalent of the hex number.

Examples

Let’s take a look at some examples to better understand the conversion process.

Example 1: Convert 3B16 to decimal

3B16 = 3×161+11×160 = 48+11 = 5910

Example 2: Convert E7A916 to decimal

E7A916 = 14×163+7×162+10×161+9×160 = 57344+1792+160+9 = 5930510

Example 3: Convert 0.816 to decimal

0.816 = 0×160+8×16-1 = 0+0.5 = 0.510

Hex (base 16)Decimal (base 10)Calculation
00
11
22
33
44
55
66
77
88
99
A10
B11
C12
D13
E14
F15
10161×161+0×160 = 16
20322×161+0×160 = 32
30483×161+0×160 = 48
40644×161+0×160 = 64
50805×161+0×160 = 80
60966×161+0×160 = 96
701127×161+0×160 = 112
801288×161+0×160 = 128
901449×161+0×160 = 144