Decimal to Hexidecimal conversion...

dellas1979

...and vice-versa.

Can someone help me understand how it is done?

Thanks

Tobias Greeshman

For Decimal to Hex, you divide by 16 and keep dividing until you can't divide any more, you store the remainders, they'll give you the hex number, read upwards to get the hex value.

150 / 16 = 9 r 6
9 / 16 = 0 r 9

150 = 96h

to do it the other way it each hex digit multiplied by 16^(pos of digit)

9 * 16 (power of 1 ) + 6 * 16 (power of zero => 1 ) = 150

dellas1979

Thanks Silas........still over my head. Baby steps please!

Tobias Greeshman

I'll assume you understand decimal to Hex, that easy just keep dividing the decimal number by 16, the hex number is all the remainders from each stage of the division.

The other way is done like so
take the hex number 2FF

(2 * 16^2) + ( 15(F) * 16^1 ) + ( 15(F) * 16^0)
(2 * 16^2) + (15 * 16) + (15 * 1)
(512) + (240) + (15)
767

Thats it, there's nothing more to it. If it still goes over your head, try it out on a piece of paper, you'll soon get the hang of it.

Tom Dunne

dellas1979 wrote:

Thanks Silas........still over my head. Baby steps please!

Start off by counting from zero to 15 (computers always count from zero, unlike humans).

So, you have 0,1,2,3...9 when you get to nine, you then start using letters. It becomes ...8,9,A,B,C,D,E,F where A=10, B=11, C=12 and so on to F=15.

Back to Decimal - what happens when you get to 9? You "reset" your counter and introduce a second digit. So 9 goes to 10. Likewise with Hex - when you get to F, you introduce another digit and reset the 'F' back to zero. So decimal 16 becomes Hex 10. You go ..E,F,10,11,12,13,14,15,16,17,18,19,1A,1B,1C... and so on.

Does this help?

yapyap

silas wrote:

For Decimal to Hex, you divide by 16 and keep dividing until you can't divide any more, you store the remainders, they'll give you the hex number, read upwards to get the hex value.

150 / 16 = 9 r 6
9 / 16 = 0 r 9

150 = 96h

to do it the other way it each hex digit multiplied by 16^(pos of digit)

9 * 16 (power of 1 ) + 6 * 16 (power of zero => 1 ) = 150

Let's say 1,000

1000/16 = 62 r 8
8/16 = 0 r 8

(8*(16^1)) + (8*(16^0)) = 136

by ure calculation 1000 = 88h --that doesn't sound right

Tobias Greeshman

you don't divide by the remainder, it's the quotient

so in your example

1000 / 16 = 62 r 8
62 / 16 = 3 r 14 (E)
3 / 16 = 0 r 3

reads as 3E8h which is 1000

(3 * 16^2)+(14(E)*16^1)+(8*16^0)
(3*256)+(14*16)+(8)
768+224+8
1000

Professional Griefer

Really sorry to bump this but it just seemed easier than making a new one.

I cannot understand this decimal to hex at all. I'm trying to convert 100 to hex. Each time I work it out I get 14, but I know the answer is 64, at least thats what the internet tells me.

What I'm doing is 100/16 = 6 remainder 4
4/16 = 0 remainder 4

Its probably something stupid I'm doing, but its wrecking my head.

Anyone help?

coylemj

You put the first remainder on the right, continue to divide by 16 and each new remainder goes to it's left until you end up with a quotient less than 16 which counts as your last remainder since clearly you cannot divide any number less than 16 by 16 so the last quotient goes in front of the string of remainders.

That is what happens on your first operation - decimal 100 divided by 16 = quotient 6 remainder 4 so the answer is Hex 64.

Just to illustrate a more complex operation: convert decimal 498 to Hex.

Divide 498 by 16 = quotient 31, remainder 2
Divide 31 by 16 = quotient 1, remainder 15 (Hex F)

So the final quotient (1) counts as a remainder since it cannot be divided by 16, it goes in front of the other two remainders and the answer is Hex 1F2

Professional Griefer

Ah, I see now. Thank you so much.

deconduo

Ix Deadmau5 wrote: »

Really sorry to bump this but it just seemed easier than making a new one.

I cannot understand this decimal to hex at all. I'm trying to convert 100 to hex. Each time I work it out I get 14, but I know the answer is 64, at least thats what the internet tells me.

What I'm doing is 100/16 = 6 remainder 4
4/16 = 0 remainder 4

Its probably something stupid I'm doing, but its wrecking my head.

Anyone help?

You divide by the first number, not the remainder:

100/16 = 6 remainder 4
6/16 = 0 remainder 6

-> 100 = 64h

Gone Drinking

Just curious why you'd need to work it out manually? Or is it just to understand it better?

GreenWolfe

Gone Drinking wrote: »

Just curious why you'd need to work it out manually? Or is it just to understand it better?

It's around exam time for the colleges, homework of some kind I'd guess.

PrzemoF

I'd suggest to learn how doc->bin and bin->dec works - it's easy.

And the rest of the crowd (oct & hex) can be created from bin on-the-fly

example (first memorize 128-64-32-16-8-4-2-1):

i.e. 100 to hex
pick 64 - it's the first smaller than 100

100-64 = 36
pick 32 - it's the first smaller than 36
36-32 = 4

so (dec) 97 = (bin) 01100001:
128 64 32 16 8 4 2 1
0 1 1 0 0 1 0 0

(bin) 0110 0001 = (hex) 64 as (bin) 0110 -> 6 and (bin) 0100 -> 4

BTW google is asking similliar questions during interviews (i.e. convert 27 to bin)