# Thread: Converting Base 10 to Base 2

1. ## Converting Base 10 to Base 2

Ok, here is a short tutorial on converting decimal numbers to binary form. Now this can be extremely important and it can also never affect you.

But having good skilz in number systems can aid you with IT stuff. you can solve problems faster without the aid of a calculator when one is not around.

Now the decimal system is based on powers of 10, duh. For example 10^0 is 1, 10^1 is 10, 10^2 is 100 etc.

| exponent 10^5 10^4 10^3 10^ 2 10^1 10^0 |
| |
| expanded 100000 10000 1000 100 10 1
| |
|
| number 3 5 2 4 8 1 |
|
| 3 * 10000 5 * 10000 2 * 1000 4 * 100 8 * 10 1 * 1 |
| |
| |
|_______________________________________________________________________________________

i take pride in my tables

anyway the binary system is base 2, meaning based on 0, and 1.

so to convert binary you do something like this

an example

decimal number = 255

ok. for smaller numbers you use 128, 64, 32, 16, 8, 4, 2, 1

so. 128 64 32 16 8 4 2 1

will 128 go into 255? yes. you put a one down

then you subtract 128 from 255.

will 64 go into 127? yes. you put a 1 down.

then you subtract 64 from 128.

will 32 go into 64? yes you put a one down.

subtract 32 from 64.

will 16 go into 32? yes you put a 1 down.

will 8 go into 16? yes you put a 1 down.

will 4 go into 8? yes you put a one down.

will 2 goin into 4?

yes you put a one down

will one go into 2? yes you put a one down.

255 to binary = 11111111

now for something with zeroes.

128 64 32 16 8 4 2 1

for example the decimal number 165

will 128 go into 165? yes you put a 1 down.

take 165 - 128. which equals 37.

will 64 go into 37? no. so you put a zero down.

then you go onto the next number with 37.

will 32 go into 37? yes you put a one down.

subtract 32 from 37 which equals 5.

will 16 go into 5? hell no. so you put a zero down and go onto the next number.

will 8 go into 5? no, so you put another 0 down. and go on.

will 4 go into 5? yes so u put a one down.

will 2 go into 1? no so you put another zero down.

will 1 go into 1? yes. so you put a one down.

thus the conversion from 165 to binary is 10100101.

now if you want large numbers than those, you simply go up more, and start with 256, or 512, or 1024 etc. the same rules apply.

now you can convert decimal to binary. extremely easy eh?

2. Sub_Proc_person_who_wrote_it_was_pissed
In my opinion it's time you went back over this!

You havent lined the exponent and expanded columns up in the explanation of decimal (despite taking pride in tables). you've also missed out a nought (zero) when
explaining 3 5 2 4 8 1 . It should be 3 * 100000 not 3 * 10000.

When binary is discussed base doesn't really mean based on 0 and
1 does it? I thought it meant that it uses two digits which are 1 and 0
(used in computers because of the state of a switch, either on or
off).

The explanation of converting binary (into what?) I understand
what is meant but that is because I have taught it so many times. I
would imagine if someone who had never done it before (converted
binary to decimal) read it, it wouldn't make any sense.

I a bit knackered at the moment and can't be bothered to
concentrate too hard so there may be other errors I haven't noticed.

Cheers anyway

3. Originally posted here by geepod
Sub_Proc_person_who_wrote_it_was_pissed
In my opinion it's time you went back over this!

You havent lined the exponent and expanded columns up in the explanation of decimal (despite taking pride in tables). you've also missed out a nought (zero) when
explaining 3 5 2 4 8 1 . It should be 3 * 100000 not 3 * 10000.

When binary is discussed base doesn't really mean based on 0 and
1 does it? I thought it meant that it uses two digits which are 1 and 0
(used in computers because of the state of a switch, either on or
off).

The explanation of converting binary (into what?) I understand
what is meant but that is because I have taught it so many times. I
would imagine if someone who had never done it before (converted
binary to decimal) read it, it wouldn't make any sense.

I a bit knackered at the moment and can't be bothered to
concentrate too hard so there may be other errors I haven't noticed.

Cheers anyway

second: when we are discussing base 2 in terms of binary, it is based on 1 and 0.

third: i had a friend read this that learned from it and can now convert base 10 to base 2, base 2 to base 10. although i had to explain the latter since it wasnt discussed.

easy on the criticism, i made some errors big deal. and the /me taking pride in my tables was a joke. notice the wink.

thanks for reading the tut, maybe you can get a job working for a newspaper being the editor or something.

btw person below, thanks for the links.

4. I wasnt trying to make anyone look bad with my criticism, actually i thought it was a good post and it was interesting, i have seen many ways for the conversion but never that one, so was impressed. I was merely pointing out errors that i obviously did in a condescending and critical manner, so I apologise profusely and thank you for your post, my criticism was not meant to be derogatory in anyway although when reading it back it does seem that way so again my apologies and thanks for the interesting post.

Geepod

5. ive got to do that for my computing homework tonight it is really easy. nicley explained er0k.
trials

6. no problem, i was only intending this thread for those who do not know binary, but know how computers work. at least to a certain extent. i realize of course if you already know it and you read this you might disagree with my teaching ethics, heh ask the debate novii.

note: i had another guy who is admittedly computer illiterate come in and read this, he can now do binary and is all pumped about it.

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