[Elliott]

Hehe I've made 5 of the 6 topics in this forum...

Just a general topic about binary perhaps. What is it and What does it do? Can anybody shed some light on this subject?

[Max]

Well, binary is a number system called "base-2". Normal numbers that we use everyday are "base-10". So the only digits in binary are 0 and 1, and instead of representing multiples of 10, they represent multiples of 2. So for a binary number, you read it like this:
16 8 4 2 1
The numbers can continue to double to the left infinitely. So what you do to read a binary number is you add up all the values that have a 1 in them. So if the number was
1 0 1 1 0
Then it would equal 22 in base-10, because 16+4+2=22.

I hope that makes some sense. Binary can also be used for creating strings of characters, but I'm not going to get into explaining that because it is a bit more involved.

[TheOnlyJaz]

And what it can do is that a certain number in binary can be assigned to each key on a keyboard. For instance, a = 97 which is 01100001 in binary. These different numbers is the ASCII. Also, 8 digits in binary is what makes up a byte, and a bit (BInary digiT) is every 0 or 1.

[Elliott]

note to self: Don't ever attempt to learn binary

That is really confusing stuff, I think I'll stick to html, css anf java actually.

[Eugine]

Well you find Binary in maths also you know...

010001010111010101100111011010010110111001100101 - "Eugine" in binary ;)

[Elliott]

lol, too much time on your hands Eugine, j/k. I think I'll stear clear of binary for the moment.

[Eugine]

Well, I just learned Binary in Information Technology class! We got it on the exams too *WHO IT WAS EASY*

[lifeform287]

People want to know about binary so I figured that I should post somethings here.
This is in ASCII though. The link for the translater is here.

A-01000001
B-01000010
C-01000011
D-01000100
E-01000101
F-01000110
G-01000111
H-01001000
I-01001001
J-01001010
K-01001011
L-01001100
M-01001101
N-01001110
O-01001111
P-01010000
Q-01010001
R-01010010
S-01010011
T-01010100
U-01010101
V-01010110
W-01010111
X-01011000
Y-01011001
Z-01011010

[Tachyon360]

Max explained it pretty well, but I'll try my best to break it up so it's easier to chew.

Binary is a very simple number base. It can be used to represent different characters in a text format, much like you can have a catalogue number for an item sold in a store.

If you want to do binary math, the first thing you need is to understand bases. The math you're used to is base 10. That is, from right to left, every space goes up by a power of 10. Remember the "1's place, 10's place, 100's place, etc" crap from 1st grade math?

That's pretty much the concept behind base 10 and a similar concept to base 2 (more on base 2 later). You can think of base 10 as denoting two things: you have 10 basic numbers to work with (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) and each step is 10 times more than the previous. Each time a number exceeds the 0-9 threshold, it's reset to 1 and added to the next place. Where does 0 come into play? Every place has a default value of 0.

So the 1's place from 1st grade math would be 10^0, and you can use anything from 0-9. The 10's place is 10^1, and you can use anything from 0-9 there as well. So 23 would be 3 in the 10^0 place and 2 in the 10^1 place. You take the values for each place and write them in descending order.

Base 2 is pretty similar, but in this case, it means that you only have two numbers to work with (1, 0) and each place is 2 times more than the previous. At this point it may get very confusing if you don't knock traditional base 10 out of your head.

To represent 1 in base 10, you just write 1. It's assumed that it represents the 10^0 space. The same thing applies in base 2. The next step is where everything you know is wrong.

In base 10, 2 is just written as 2. It still falls into the 10^0 place, since you have 10 numbers to use (one again, 0-9). If it would be 10 or more, you'd have to push the first digit into the next place. In base 2, you only have 0-1 to work with. 2 is greater than that, so it goes into the next place. Thus, the number 2 in base 10 would be written as 10 in base 2.

Confusing? Bear with me. It should make some more sense soon. Remember how I said 23 is the base 10 representation of what we know as the number 23? Remember how I said you take the value for each place and write them in decending order?

Well, keep that in mind. The for 10 (in base 2) value for the 2^0 place is 0. The value for the 2^1 place is 1. Why? Because each space is 2 times more than the previous. 2^0 in base 10 is 1. 2^1 in base 10 is 2. 2^2 in base 10 is 4. Etc. So, you have 10 meaning 2, since the 2^0 place is 0 and the 2^1 place is 1.

WTF? That doesn't make sense! How could 10 = 2?

Actually it does make sense. 1 and 0 are just symbols to represent the value of a place. If we'd replace 0 with A and 1 with B, then BA would mean 2. Like I said, get the idea of traditional math out of your head. It's all about the bases. The symbols are just used to mark off certain values for each place.

Good. Now that that's settled, let's get on to the number 3 in base 10. How would you write it in base 2? You'd write it as 11 (or BB, if that would help you visualize it). Why is that? 2^0 has a value of 1. 2^1 has a value of 1. It is therefore 11. In base 10, 3 still doesn't exceed the 0-9 range, so it still remains in the 10^0 place.

Now we get to 4. Remember how 2 was too big for the 2^0? 4 is too big for the 2^1 place. It's like adding 50 and 50 in base 10. Added together, they exceed the 10^1 place, so the counter is started over at 1, and that one goes into the 10^2 place. Known in 1st grade math as the 100's place. 4 in base 2 would therefore be 100 (or BAA if it makes it easier - I can't stress it enough that numbers you can read aren't truly numbers, but rather symbols used to represent numbers).

5 in base 10 would be 101 in base 2. 6 in base 10 would be 110 in base 2. 7 would be 111. (This situation is analogous to 999 in base 10. One more and it's 1000. In base 2, 1 more than 111 would be 1000). 8 in base 2 would be 1000.

So to sum it up:

Base 10 is: ... 10000's place, 1000's place, 100's place, 10's place, 1's place.
Base 2 is: ... 32's place, 16's place, 8's place, 4's place, 2's place, 1's place.

base 10 | base 2
0 | 0
1 | 1
2 | 10
3 | 11
4 | 100
5 | 101
6 | 110
7 | 111
8 | 1000
9 | 1001
10 | 1010
11 | 1011
12 | 1100
13 | 1101
14 | 1110
15 | 1111
16 | 10000
... | ...


____________________________________________________________________
Once you understand how base 2 works, there's a shortcut. 1 is true and 0 is false. Each place is 2 times more than the previous. Add the places that have a value of true, ignore those that are false. So...

1000110

1__0__0__0__1__1__0
64_32_16_8__4__2__1

64_x__x__x__4__2__x

64 + 4 +2 = 70

1000110 in base 2 would therefore be 70 in base 10.

[Elliott]

I see this as an invaluble resources for anyone wanting to learn about binary.

[Tachyon360]

Did it do what it was supposed to?

If not, then it's a worthless resource.