# Hex to Decimal Converter

## 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

Example #3

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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