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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:
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
Hexadecimal to Decimal Conversion Table
Use the following table to help you with your hexadecimal to decimal conversions:
| Hex (base 16) | Decimal (base 10) | Calculation |
|---|---|---|
| 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 | – |
| 10 | 16 | 1×161+0×160 = 16 |
| 20 | 32 | 2×161+0×160 = 32 |
| 30 | 48 | 3×161+0×160 = 48 |
| 40 | 64 | 4×161+0×160 = 64 |
| 50 | 80 | 5×161+0×160 = 80 |
| 60 | 96 | 6×161+0×160 = 96 |
| 70 | 112 | 7×161+0×160 = 112 |
| 80 | 128 | 8×161+0×160 = 128 |
| 90 | 144 | 9×161+0×160 = 144 |