## Hexidecimal to decimal

Mathematics and Science; the subtle and ubiquitous arts

### Hexidecimal to decimal

Can somone please give me an example on how to convert a hexidecimal number to a decimal number? i have been looking around but still don't get it.

0x62ee6190

is the problem i am trying to solve it's from the pico challenge, i could get the answer and pass it easily using an online converter but i want to be able to convert it myself. the steps i'm doing are as follows and i'm leaving out the 0x at the beggining as those just tell me that it's hexidecimal ( ^ <--- that arrow means root right? )

6 2 14 14 6 1 9 0

1) 6 * 16 ^ 7 = 254

2) 2 * 16 ^ 6 = 78

3) 14 * 16 ^ 5 = 500

4) 14 * 16 ^ 4 = 448

5) 6 * 16 ^ 3 = 166

6) 1 * 16 ^ 2 = 22

7) 9 * 16 ^ 1 = 144

8) 0 * 16 ^ 0 = 0

The answer i get after adding all those up is 1612 but in the converter online the answer is 1659789712 and i don't understand why it's such a high number, i know i must be missing a step.

Thank you to anyone who explains this in advance
tripbeam
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### Re: Hexidecimal to decimal

Check your math, start with line #6. What's 16 squared? Certainly not 22. Go from there for line 5 on backwards. I haven't verified the rest, just a glaring issue with line 6.
akorshikai
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### Re: Hexidecimal to decimal

Yeah, akorshikai is right, I found that calculating 16^7*6 you get a number close to the online converter, confirming that your math is the problem.

Edit: I can now confirm that the math is indeed the problem, I got the same answer as the online converter by doing the calculation correctly.
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cyberdrain
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### Re: Hexidecimal to decimal

Alright thanks, i will try that when i get back too it.
tripbeam
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### Re: Hexidecimal to decimal

Let's take an example Hexadecimal number: 8A4C

The first thing you need to realize is this is base 16, and we want it in base 10.
To do this, count the amount of digits in the number and subtract one, in this case "8A4C" would be 3.
Next, convert all the characters in the number to their base 10 equivalent.
This give us: 8, 10, 4, 12

This is where the number 3 comes in handy, as each number needs to be given the power of it's current position.
For example, 8^3, 10^2, 4^1, 12^0

Now, the next step would be to make sure you are multiplying by 16:
8*16^3, 10*16^2, 4*16^1, 12*16^0

8*16**3 = 32768
10*16**2 = 2560
4*16**1 = 64
12*16**0 = 12

Last thing to do is add the values
32768+2560+64+12 = 35404

For a live demonstration, check this out:
http://repl.it/3K8
Here is the code from above, if you are scared of links (Ruby)
Code: Select all
`hex = {'a' => 10, 'b' => 11, 'c' => 12, 'd' => 13, 'e' => 14, 'f' => 15}value = '62ee6190'numbers = value.split('')@total, @c = 0, ((value.length)-1)numbers.each do |n|  if n =~ /[[:alpha:]]/    n = hex[n]  else    n = n.to_i  end  puts "#{n} * 16 ** #{@c} = #{n * 16 ** @c}"  @total += (n * 16 ** @c)  @c -= 1endputs @total`

For those that know
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-Ninjex-
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### Re: Hexidecimal to decimal

-Ninjex- wrote:Let's take an example Hexadecimal number: 8A4C
...
Last thing to do is add the values
32768+2560+64+12 = 35404

Thanks a lot Ninjex. I was struggling on this as well but this pretty much explains it.
One question tho, why do you count the numbers from right to left? Wouldn't it be more logical that the 8 is in the 1st(0th) posistion? That way you get:

8*16^0 = 8
10*16^1 = 160
4*16^2 = 1024
12*16^3 = 49152

8+160+1024+49152 = 50344
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Randoph
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### Re: Hexidecimal to decimal

Randoph wrote:One question tho, why do you count the numbers from right to left? Wouldn't it be more logical that the 8 is in the 1st(0th) posistion? That way you get:

8*16^0 = 8
10*16^1 = 160
4*16^2 = 1024
12*16^3 = 49152

8+160+1024+49152 = 50344

Well, 8 is the first digit, but it has the highest power.
Just like the decimal value '110' break it down
1 * 10 ** 2 = 100
1 * 10 ** 1 = 10
0 * 10 ** 0 = 0

100 has a power of 2 (two places away from the first digit)
10 has a power of 1 (one place away from the first digit)
0 has a power of 0 (it's the first digit)

http://en.wikipedia.org/wiki/Power_of_10

So for hexadecimal, we just substitute the 10 with 16

If you do it in reverse, you will be telling it that 100 has a power of 0, 10 has a power of 1, and 0 has a power of 2, which is false, and will lead to an incorrect result as you can see from your above example.

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-Ninjex-
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### Re: Hexidecimal to decimal

-Ninjex- wrote:
Randoph wrote:One question tho, why do you count the numbers from right to left? Wouldn't it be more logical that the 8 is in the 1st(0th) posistion? That way you get:

8*16^0 = 8
10*16^1 = 160
4*16^2 = 1024
12*16^3 = 49152

8+160+1024+49152 = 50344

Well, 8 is the first digit, but it has the highest power.
Just like the decimal value '110' break it down
1 * 10 ** 2 = 100
1 * 10 ** 1 = 10
0 * 10 ** 0 = 0

100 has a power of 2 (two places away from the first digit)
10 has a power of 1 (one place away from the first digit)
0 has a power of 0 (it's the first digit)

http://en.wikipedia.org/wiki/Power_of_10

So for hexadecimal, we just substitute the 10 with 16

If you do it in reverse, you will be telling it that 100 has a power of 0, 10 has a power of 1, and 0 has a power of 2, which is false, and will lead to an incorrect result as you can see from your above example.

Thank makes a lot of sence.
A little rebellion now and then ... is a medicine necessary for the sound health of government.
-Thomas Jefferson

Randoph
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### Re: Hexidecimal to decimal

Thank you guys! i finnaly understand it, took me ages
tripbeam
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### Re: Hexidecimal to decimal

tripbeam wrote:Thank you guys! i finnaly understand it, took me ages

For those that know
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-Ninjex-
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