Re: A86: Tutorials
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Re: A86: Tutorials
not stupid at all. it took me forever to understand it. here is how i
learned it, this was posted by someone else on the list
<<Number bases scare entry level asm programmers bad. However, they're not
that hard to understand. Basically, number bases are ways of representing
numbers or values. This is a pretty long message, but it should be fairly
easy to understand.
Take the value twelve. I write it in english since '12' is base ten.
"Twelve" in english does not mean that you have to think of it as 1, then 2.
Twelve simply means twelve things or a value of twelve. You have to
remember that when converting to a different base, the value is still the
same. A new base is just a different way to represent it. Anyways:
twelve:
in base 10, that would be: 12
If you remember back from grade school, each digit has a place with a name.
In the case of '12', there is a '1' in the tens place and a '2' in the ones
place. Remember that stuff? Well, the third digit would be the hundreds
place, then the thousands place and so on.
base 10: 2439
is a '2' in the thousands place, a '4' in the hundreds place, a '3' in the
tens place and a '9' in the ones place. Think about it like this:
there are 2 "thousands"
and 4 "hundreds"
and 3 "tens"
and 9 "ones"
2 * 1000 + 4 * 100 + 3 * 10 + 9 * 1 = 2439. You're probably wondering what
the heck the point of that was. Well, now you can see why they name the
digit places as they do. The thousands place is called what it is because
it holds the number of "thousands" in the number.
Notice that the "places" are named by the following values:
10^3 10^2 10^1 10^0
10^0 being the ones place since 10^0 = 1 obviously.
Now, let's move on to a different base... like 16 (hexidecimal). by the
way, the word hexidecimal means 6(hex) and 10(decimal) which is base 16. In
base 16, we have the following:
16^3 16^2 16^1 16^0
Now this one is trickier to read. We're used to all those zeros from our
base 10 life that we live. But in base 16, we have:
the 4096's place
the 256's place
the 16's place
and the 1's place (there is a ones place in all bases)
So lets say you have a number in base 16 ---> 35
that's a 3 in the 16's place and a 5 in the 1's place.
thus there are 3 sixteens, and 5 ones.... or in other words: 53
so 35 in hex is 53 in decimal.
another thing to remember is that the number of possible values per digit
changes based on the base. how many different values could be in the 1's
place in base 10? the answer: 10! 0, 1, 2, 3, 4, 5, 6, 7, 8, 9...
that's 10 possible values for a digit to have. In base 16, we have 16
possible values per digit. Unfortunately since we all live in a world
dominated by base 10, no other symbols were invented for subsequent values.
Thus, we use the alphabet letters A through F to represent our otherwise
unrepresentable 6 values.
so what is the value of the hex number: 2b ??
2 sixteens and B ones. that's 43. remember that B is a value of eleven in
a single digit. One way to see why is to count. In base 10, we go "0, 1,
2, 3, 4, 5, 6, 7, 8, 9, THEN 10". Every other base is the same way. We
don't move on to the next digit until we have counted out all 10 values. In
the case of base 16, we don't move onto the next digit until we have counted
16 values. "0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, THEN 10". Your
probably saying. Huh? 10? where did that come from? Well, remember that
F is 15. What is 10 in base 16? that's 1 sixteen and 0 ones. which is
16.
so F is fifteen, and 10 is sixteen....hexidecimally speaking, of course.
you should really read 10 as "one, zero" and not "ten" otherwise it'll screw
you up bad.
Ok, by now the answer to your question should be clear but let's go over it
anyway.
10 in decimal (or base 10) is A in hexidecimal. remember? 0, 1, 2, 3, 4,
5, 6, 7, 8, 9, A, B ..." A is the tenth value and thus A is ten. note
that it should be written as:
Ah
or
$A
since those are standard ways to write hex (and your assembler won't
understand what the heck you mean unless write it one of those ways).
Now, $10 is different. that's a hex number.
$10 (or 10h) is 1 sixteen and 0 ones. Thus, $10 in hex is 16 in base 10.
All the rest of the number bases follow the same rule:
Base^3 Base^2 Base^1 Base^0
Just insert the base you want to use. For bases higher than 10, you must
use something to fill in the missing values (although the standard is to use
letters). For bases below 10, just use less of the normal numbers. Like
for base 8 you'd only use 0-7. And remember that Binary is Base 2, if you
ever feel like messing around with that.
Hope this helped =).
-Justin Karneges [Infiniti]>>
that should help. its not that hard after you read this though.