You want to display the hexadecimal number: $$ABC_{16}$$ in decimal form. What hexademical
number should you add to this so that it will display in hexadecimal the same as if it was converted to decimal? For example, $$A_{16} = 10_{10} and A_{16} + 6_{16} = 10_{16},$$ so to make "A" display the same as decimal, you would add $$6_{16}$$

Question

You want to display the hexadecimal number: $$ABC_{16}$$ in decimal form. What hexademical
number should you add to this so that it will display in hexadecimal the same as if it was converted to decimal? For example, $$A_{16} = 10_{10} and A_{16} + 6_{16} = 10_{16},$$ so to make "A" display the same as decimal, you would add $$6_{16}$$

asnaseer · Answer

first step is to convert $ABC_{16}$ into decimal.
what do you get for this?

anonymous · Answer

Um, I'm not used to hexadecimals at all. I'm only used to decimals and this is a new topic to me.

asnaseer · Answer

I suggest you first study this: http://www.mathsisfun.com/hexadecimals.html and then come back to this question.

anonymous · Answer

From a quick google search though, I think that it's 2748

anonymous · Answer

Did I get it right?

asnaseer · Answer

it better to learn the concept than to reply on google.

I would really advise you to first study the link I gave you and then come back, otherwise you will just get stuck in the next steps.

asnaseer · Answer

*to rely on google

anonymous · Answer

Ok. I learned how to convert hexadecimal to decimal and the columns and counting system before, but do I need to know "the point"?

phi · Answer

the positions in hex are powers of 16
$$ 16^2 16^1 16^0 $$  
for the first 3 digits.   
to accomodate numbers 10 through 15 we use A,B,C,D,E,F
A 10   B 11 C12  D13  E14 F15
so ABC  in hex is 
$$A*16^2 + B*16^1 + C*16^0 $$
or
10*256 + 11*16 + 12*1 = 2748

anonymous · Answer

Yeah. I understand that per. But in the example, it says:
$$A_{16} + 6_{16} = 10_{16}$$ which I can't seem to figure out why it works.

phi · Answer

To find what to add to ABC hex to get 2748 hex, we subtract (in hex!)
$$ 2748_{16} - ABC_{16} $$
an interesting exercise, but you borrow 16 rather than 10...

phi · Answer

$$ A_{16} + 6_{16}  =  16_{10} $$
but 16 is the next power of 16, so in hex, 
$$ 10_{16} $$

anonymous · Answer

Oh ok.

phi · Answer

so F+F = (15+15 decimal=30 decimal= 1*16+14 --> 1E hex

phi · Answer

of course, you could memorize the addition table for hex, or count on your 16 fingers(!)

anonymous · Answer

2748
-ABC
-----
1C8C
I that it?

phi · Answer

that's what I got

anonymous · Answer

Alright. That's what the answer key says too. Thanks! It was pretty simple once I switched the system of 10 to 16 :)