Introduction to Binary

[God-The-RapistV2.0]

So GRM and I were watching BILL NYE THE SCIENCE GUY (we own every episode ever made) and it was about computers. We got to the part in the show where they explained how counting in Binary worked.

I thought that it would be cool to teach every here who doesn't know how to count in binary how to do so. It is really a simple thing.

Binary works in Switches. Off = 0 and On = 1. Counting in binary is done so by adding together ON switches based on their position. As an example:

0 = 0

That is that Zero is equal to Zero. Pretty simple stuff. We can then assume that:

1 = 1

That is that One is Equal to One.

Counting Higher than One is a little more complicated because bits can't go higher than ONE so we need to express to the computer that you want more than one bit. Now Binary is strange as you add to the LEFT not the RIGHT as you are probably used to. As an example:

10 = 2

That is we added a Second switch and it is ON and the first switch is OFF so number Two is On. We then use an addition system. So if Switch Number TWO is on and Switch Number ONE is on that is ONE plus TWO.

11 = 3

That is to say that 10 + 1 = 11 or 3.

Since we now have reached the maximum Number of switches to be ON that is that Switch One and Switch Two are both on we then must add a another switch if we wish to count higher.

100 = 4

And this cycle continues using the same addition system.

101 = 5

OR 100(4) + 1(1) = 5. And so on and so forth.

Now the next step is slightly confusing to some people and where a lot of people just give up but if you have followed along so far then there isn't much more to learn.

So far we have just been adding switched and ones together and most of this is simple but to form the next number (6) it takes a little bit of memorizing.

110 = 6

Or; 100(4) + 10(2) = 6

You have to memorize the binary code for Two (10) and then add it two the binary code for 4 (100). If you can get past this step then you can pretty much count in Binary, with a little time and practice.

1 - 10 in Binary:

1
10
11
100
101
110
111
1000
1001
1010

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[Roland Karloseth]

Tell me, exactly what does freedom mean...

I miss Bill Nye the Science Guy! That show was awesome!

Anywho, I've tried to learn Binary before, actually. With no success.

...if I'm not free to be as twisted as I want to be?

 

[God-The-RapistV2.0]

Did this help you?

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[Roland Karloseth]

Tell me, exactly what does freedom mean...

Actually, it does make it easier to understand. Maybe now I'll know what they are talking about when I retake my computer lit. class.

...if I'm not free to be as twisted as I want to be?

 

[Bassios]

I had to learn to do binary arithmetic on my Electronic Engineering course. Can't remember it properly though.

Here's an odd thing though, on an 8-bit binary sequence (00110011, and such like), if it leads with a 1 (10110011) it's a negative number. If you want to use the 256-position bit, you have to add a second set of 8 bits so that it doesn't show up as a negative number.

whee

 

[God-The-RapistV2.0]

Bass20XX

I had to learn to do binary arithmetic on my Electronic Engineering course. Can't remember it properly though.

Here's an odd thing though, on an 8-bit binary sequence (00110011, and such like), if it leads with a 1 (10110011) it's a negative number. If you want to use the 256-position bit, you have to add a second set of 8 bits so that it doesn't show up as a negative number.

whee

Equations in binary make my head hurt. Addition and Subtraction are pretty much the extent of my skills. Letters also bother my brain but only because I haven't actually taken the time to memorize every letter or punctuation mark.

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[Bassios]

One of my friends in college could recite his name in binary at one point. Thankfully he only had 4 letters to remember. xd

He's forgotten it now.

 

[Xikrai the Risen]

I love binary thanks to doing it for 2 years. There's some other nifty tricks to it. Especially for counting.
Here's basically what binary means, each bit(digit) position is a different power of 2. The 1 spot is (1 or 0)*10^0 and from there it goes on. So, each spot represents a different value. So, the decimal equivalent is the addition of the value of each spot. Up to 8 bits here are the values.

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

So, basically from there you can see that each next spot doubles from it's previous spot. There's so much more you can do with binary that is fun. Addition and subtraction are really fun and grey code and karnaugh maps. But I'll stop.

Oh! And I almost forgot another trick.

Let's say you have 4 bits, you can count very easily with out memorizing combos.

0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111

Now look at the columns. See how in the 1 position the 1 and 0 alternate every other number. Then the 2 position the 1 and zero alternate ever 2 numbers. It increases from there every bit position.
 

[God-The-RapistV1]

Yes you are right just like each new numerical place in 'regular' counting has it's own value so does Binary.

When you are talking about common numbers the places are Ones, Tens, Hundreds, etc. For example:

One hundred and Forty Three = 143 = One "Hundred" Four "Tens" Three "Ones"

This is actually an unexpressed equation which is written out would look like: ([1]x100)+([4]x10)+([3]x1)

Binary also has this same method but when you are talking about binary it is a growth pattern based on 2. So the first Column would be 2^0 and then 2^1 then 2^3 etc. So when you are talking about a number like lets say 18 the binary would word out to be 10010 and properly expressed that would be

([1]x2^4)+([0]x2^3)+([0]x2^2)+([1]x2^1)+([0]x2^0)

OR

16+0+0+2+0 = 18

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[YunieCookie]

The best I can do is count in binary on my fingers.. It's pretty cool, and can confuse some people because when you get to four, they think you're flipping them off xd  

[Xikrai the Risen]

Even though that's how every number system pretty much works. I just can't think of base-10(normal system) in the same way as binary. But I still can do Octal and Hex that way. At first I wondered why I got learn HEX, then I got to my college class this semester on microprocessors and microcontrollers and it really makes programming a lot easier.

For those that don't know Octal is a number system where the digits go 1-7 and go by powers of 8.

And Hex is a number system where the digits go 1-15 essentially. 1-9 are regular numbers, then 10-15 get represented by A-F. Where this comes in handy is when you wanna work with binary and not type in all those 1's and 0's.

Example: 1010 1001 would be A9. Each group of 4 starting from the left gets its own HEX digit. And unlike binary coded decimal, those 2 numbers have the same decimal equivalent.

GTR: You have made quite possibly my favorite thread ever here. Sure, not everyone will appreciate binary. But, people don't realize that this is what makes their computers tick. I'm really just starting to learn that in school. It kinda blows my mind since I'm just starting though that people could even design computers.

 

[^^Psycha^^]

********! It looks so consfusing all you guys are talking about  

[God-The-RapistV1]

^^Psycha^^

[TurtIe Tracks]

I learned binary code through this CD, where they introduced it (you could switch on and off switches and see what value there'd be) and me being the little nerd with no life I was, I spent the next day teaching myself it. And I spent like the next week or two writing down all the places (getting to the millions) on our big family whiteboard. I'm no longer sure if that's a good or bad thing, since I really had no use for it... But then I learned about bytes and stuff. Twas pretty nifty. Also once you know binary code hexadecimal is a lot easier to get.

Anyway the point is if a 2nd/3rd grader can learn binary code then so can you! [/bragging]

PS: Bill Nye the Science guy has the same birthday as me! biggrin  

[God-The-RapistV1]

I`m not going to hide it. I`m bumping my thread because it`s dropping and I don`t like to see my awesome counting thread disappear. There are plenty of people here who understand Binary enough that we can start something cool and just a little bit interesting (Pun intended)

SO!

Addition in Binary:

Addition is the most simple of all the arithmetic equations for Binary.

0 + 0 → 0
0 + 1 → 1
1 + 0 → 1
1 + 1 → 0, carry 1

So lets see if you can add in Binary:

10 + 100 = ?

101 + 111 = ?

10110 + 1010 = ?

Also for extra credit: Show the full equation for each Bit code and convert into 10-Base numbers.

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Art By: La Belle Isolde