Hexadecimal - Help me with the math please

[Bill in SD, CA]

I'm trying to understand hexadecimal conversions. It's one thing to input and convert on a calculator and another to be able to do and understand it myself.

Take the number 11453 for instance - in hex it is 2cbd.

How do I do it manually? I'm really lost here. What I came up with isn't remotely close. I had five places and when I inputted my hex number into the converter to check my work I almost fell off the chair.

Thanks,

Bill

[Wannabe Z]

OK. Hexadecimal isn't really that hard, you just have to change your way of thinking about numbers. Hexadecimal is base 16, meaning you multiply the digit in each spot times 16 raised to the power of the spot (phew). OK, say you have the number 111h (the h designates the number as hexadecimal). Your answer would be 1 x 16^0 + 1 x 16^1 + 1 x 16^2, which is 1 + 16 + 256 which is 273. If you need more clarification just reply back.

[Bill in SD, CA]

Thanks! Clarity starting to come. Focus Daniel-San ... focus!

Can you walk me the other way dec to hex?

Bill

[Wannabe Z]

OK, the other way is a little harder. I do it this way tho. Say I have the number.... 273. I would say, "OK I have one 256 (16^2), one 16 (16^1), and one 1 (16^0), soo.... it would be 111h." If you had, say, 524 tho, you could do the same thing. Two 256 (524 - 512 = 12), no 16's, and 12 ones, so the number would be 20ch.

[Bill in SD, CA]

Wait, I think I got it. I may be doing this the hard way but it worked. If there is an easier way let me know. I just want to understand it.

11453 divided by 16 until I get a number less than 16.

That's the first number - in this case 2 point whatever.

2*16^3= 8192 sub that from 11453 = 3261

3261 divided by 16 until less than 16 - > 12 point whatever = C

and so on until I get to the end.

Right?

Bill

[Wannabe Z]

Well, your way is the "hard" way, but its also the correct way. I just memorize what each spot is worth, like the first is worth 1, second is 16, third is 256, fourth is 4096, and so on and so forth. The same way of thinking can be applied to any number system, by the way, so now you know binary, if you didnt already.

[Epidemic]

4096	256	16	1		
2	c	b	d		
2	12	11	13		
8192	3072	176	13	Sum	11453

Break each digit out into your 4 places
The D is the 1's column so 13*1 = 13
2nd column B is 11*16 =176
3rd column is C 12*256=3072
4th column is 2 2*4096=8192

add all places up
13+176+3072+8192=11453

[Wannabe Z]

Precisely. You are a genius.

[Bill in SD, CA]

At age 51 memorizing anything is getting harder.

If all I had was a pencil and paper and no calculator I am now good to go!

Kind of relates to this thread don't you think?

Thanks guys! I'm in your debt!

Bill

[Wannabe Z]

Hey, it's my pleasure to help someone who was in the same situation I was.

Oh, and I despise math. :-)