How to convert from hex to decimal
A regular decimal number is the sum of the digits multiplied with a power of 10.
137 in base 10 is equal to each digit multiplied with its corresponding power of 10:
13710 = 1×102+3×101+7×100 = 100+30+7
Hex numbers are read the same way, but each digit counts the power of 16 instead of the power of 10.
For hex numbers with n digits:
dn-1 … d3 d2 d1 d0
Multiply each digit of the hex number with its corresponding power of 16 and sum:
decimal = dn-1×16n-1 + … + d3×163 + d2×162 + d1×161+d0×160
How to Calculate Hexadecimal to Decimal
Hex is a base 16 number, and decimal is a base 10 number. Therefore, we need to know the decimal equivalent of every hex number digit.
Here are the steps to transform hex to decimal:
- Get the decimal equivalent of hex from the table.
- Multiply every digit with 16 power of digit location.
- (zero-based, 7DE: E location is 0, D location is 1, and the 7 location is 2)
- Sum all the multipliers.
Here is an example:
7DE is a hex number 7DE = (7 * 162) + (13 * 161) + (14 * 160) 7DE = (7 * 256) + (13 * 16) + (14 * 1) 7DE = 1792 + 208 + 14 7DE = 2014 (in decimal number)
Example #1
3B in base 16 is equal to each digit multiplied with its corresponding 16n:
3B16 = 3×161+11×160 = 48+11 = 5910
Example #2
E7A9 in base 16 is equal to each digit multiplied with its corresponding 16n:
E7A916 = 14×163+7×162+10×161+9×160 = 57344+1792+160+9 = 5930510
0.8 in base 16:
0.816 = 0×160+8×16-1 = 0+0.5 = 0.510
Hex to the decimal conversion table
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 |
11 | 17 | 1×161+1×160 = 17 |
12 | 18 | 1×161+2×160 = 18 |
13 | 19 | 1×161+3×160 = 19 |
14 | 20 | 1×161+4×160 = 20 |
15 | 21 | 1×161+5×160 = 21 |
16 | 22 | 1×161+6×160 = 22 |
17 | 23 | 1×161+7×160 = 23 |
18 | 24 | 1×161+8×160 = 24 |
19 | 25 | 1×161+9×160 = 25 |
1A | 26 | 1×161+10×160 = 26 |
1B | 27 | 1×161+11×160 = 27 |
1C | 28 | 1×161+12×160 = 28 |
1D | 29 | 1×161+13×160 = 29 |
1E | 30 | 1×161+14×160 = 30 |
1F | 31 | 1×161+15×160 = 31 |
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 |
A0 | 160 | 10×161+0×160 = 160 |
B0 | 176 | 11×161+0×160 = 176 |
C0 | 192 | 12×161+0×160 = 192 |
D0 | 208 | 13×161+0×160 = 208 |
E0 | 224 | 14×161+0×160 = 224 |
F0 | 240 | 15×161+0×160 = 240 |
100 | 256 | 1×162+0×161+0×160 = 256 |
200 | 512 | 2×162+0×161+0×160 = 512 |
300 | 768 | 3×162+0×161+0×160 = 768 |
400 | 1024 | 4×162+0×161+0×160 = 1024 |
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