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Hex to Decimal Converter



Hex to Decimal


What's the Hex System?

The hex system, or hexadecimal, is a base 16 number system. Because the decimal system has only 10 digits, the additional 6 digits are represented by the first 6 letters in the alphabet. For example, a hex value of B would be represented in decimal form as 11, or a binary value of 1011. It is an easy way to express binary numbers in modern computers where a byte is usually defined as containing eight binary digits.

What's the Decimal System?

The decimal system is one of today’s oldest and most commonly used numbers systems. It is also known as base 10 numbering because it is based on 10 single digits:0,1,2,3,4,5,6,7,8,9. For example, a decimal value of 11 would be represented as a hex value of B, or as a binary value of 1011.

Convert hexadecimal to decimal

Now, how do you manually convert hex to a decimal? First, you must know that all the letters in a hex have decimal equivalents as listed in the table below.

Hexadecimal to Decimal 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

 


There are other number system tables with more values for octas, hexes, decimals, and binaries, but the table above provides everything we need to understand how to convert hexadecimal to decimal.

How do you manually convert from hex to decimal?

To manually convert a hexadecimal to a decimal, you must start by multiplying the hex number by 16. Then you raise it to a power of 0 and increase that power by 1 each time according to the equivalent hexadecimal number.

We start from the right of the hexadecimal number and go left when applying the powers. Every time you multiply a number by 16, the power of 16 increases.

When converting a hexadecimal C9 to decimal your work should look like this:

Example

9 = 9 * (16 ^ 0) = 9

C = 12 * (16 ^ 1) = 192

Then, we add the results

192 + 9 = 20110  decimal

Let’s try to understand how:

  • First, we converted all of our hex numbers into their decimal equivalents. C is equal to the decimal 12 (see table above) and 9 is equal to the decimal 9.
  • Then we multiplied the numbers 12 and 9 starting with the last number in the question by 16 and its power. Remember, the powers start at zero.
  • Our first multiplication had 0 power and the second multiplication had 1. If there were a third, it would have had a power of 2.
  • The (^) symbol represents "raised to the power of." Therefore, the first terms in brackets read, "16 to the power of 0." This means that sixteen were multiplied by themselves zero times. Anything raised to zero power is 1. Therefore, 9 were multiplied by one.
  • In the second bracket, the term read, "16 to the power of 1." A number raised to one's power is equal to that number. Therefore, 12 were multiplied by 16. We got 192 when we multiplied these.
  • We then added the results to get our number of decimal equivalents, which was 201.

What if you don’t want to convert hex to dec manually?

No worries! We have hex to int converter that can help you out in converting hex to decimal online. Prepostseo hex to decimal calculator has advanced and quick interface of converting base 16 to base 10. Moreover, you can convert decimal to hex using our online dec to hex converter. Apart this tool, we offer text to binary, decimal to binary, binary to decimal, and binary translator for free conversion.

How Does Hex to decimal Converter Work?

The online hex converter tool allows you to instantly convert hex to decimal numbers. Hexadecimal converter is a quick solution for hex to number or simply hex conversion. 

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