We are used to dealing with the decimal system, 10 characters:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Binary only uses two characters:
0, 1

Lets start converting, let's pick the Decimal number 43.

Then we make something like this to help with the conversion(when you're pro you can just imagine it in your head):

128 | 64 | 32 | 16 | 8 | 4 | 2 | 1

Why these numbers?
- You can create ANY number you want(up to 256) by adding any of these, want 10? add 8 + 2, want 5? add 4 + 1.

So, lets start from the left side.
- Is 43 bigger or equal to 128? No, so we skip to the next number and place a 0 in place of 128, table now looks like this:

Code:

128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 0

- Is 43 bigger or equal to 64? No, so again, we skip to the next number and place a 0 in place of 64, table now looks like this:

Code:

128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 0 | 0

- Is 43 bigger or equal to 32? Yes, so we do 43 - 32 = 11, and put a 1 under 32.

Code:

128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 0 | 0 | 1

Is 11 bigger or equal to 16? No, so 0 goes under 16.

Code:

128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 0 | 0 | 1 | 0

Is 11 bigger or equal to 8? Yes, so 11 - 8 = 3 and 1 goes under 8.

Code:

128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 0 | 0 | 1 | 0 | 1

Is 3 bigger or equal to 4? No, so 0 goes under 4.

Code:

128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 0 | 0 | 1 | 0 | 1 | 0

Is 3 bigger or equal to 2? Yes, so 3 - 2 = 1 and 1 goes under 2.

Code:

128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 0 | 0 | 1 | 0 | 1 | 0 | 1

Is 1 bigger or equal to 1? Yes, 1 goes under 1.

Code:

128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1

So there you go, 43 is 00101011 in binary, how can we check if this is true?
- Add all the numbers that have a 1 under them.

1 + 2 + 8 + 32 = 43, correct

Now do this number on your own: 78

Spoiler: Answer

01001110 Congrats if you got this! If not, don't worry, you'll get there.

Hope this tutorial was helpful, I searched a little and couldn't find another one so i decided to post it, also not sure if the section is the most suited.

(08-21-2011, 02:10 AM)1llusion Wrote: Wow this is awesome!!! I did binary myself, but in a different, more complicated way. Thank you for sharing!