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  #1  
Old April 27th, 2004, 04:29 PM
NanoWarrior NanoWarrior is offline
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I can't make any sence out of this gragh

I found this on a site,

Look at the table. One bit counts to two numbers, two bits count to four numbers, three bits to eight numbers, four bits to 16 numbers, five to 21, six to 64, seven to 128 and finally, one byte (8 bits) counts to 256 numbers.

Decimal Binary Representation
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

to me it seems like what the info on top is saying is conflicting with its gragh, on top it says 2 bits represents 4 numbers which makes sence but the gragh says 2 bits it can represents 10 numbers.

Is it that this gragh is bad or I am not getting what it means?

thanks

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  #2  
Old April 27th, 2004, 05:44 PM
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Actually, where it says that 2 represents 10, it actually means that the number 2 is represented in binary as 10 (2+0=2). Similarly, where it says 4 represents 100, this actually means 4's binary equivelant is 100 (4+0+0=4). 15's binary equiv. is 1111 (8+4+2+1=15). 255's is 11111111, or 128+64+32+16+8+4+2+1=255.

At least, this is my interpretation given the information you posted.
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  #3  
Old April 27th, 2004, 05:50 PM
NanoWarrior NanoWarrior is offline
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Thankd for trying to help but I still don't understand

Last edited by NanoWarrior : April 27th, 2004 at 05:52 PM.

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  #4  
Old April 28th, 2004, 12:24 AM
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The binary system counts using powers of 2. So from left to right, the first position(bit) is 2^0=1, the next bit is 2^1=2, then 2^2=4 and so on. A one in a given position means to add that power of two, a zero in that position means leave that power blank.
So, if you had the binary number 1001, it means you have 2^0 (leftmost bit) + 2^3 (rightmost bit)= 9.
http://www.webopedia.com/TERM/b/binary.html is another explaination of binary.
The table is not showing how many numbers can be described with a given number of bits, it is showing the binary representation of the decimal numbers on the right.
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  #5  
Old April 28th, 2004, 06:13 PM
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You need one of these: http://www.thinkgeek.com/cubegoodies/lights/59e0/

101010 is 42.

read it right to left.

The rightmost is 0
0 x 1 = 0

Second from right is 1
1 x 2 = 2

Third from right is 0
0 x 4 = 0

Fourth from right is 1
1 x 8 = 8

Fifth from right is 0
0 x 16 = 0

Sixth from right is 1
1 x 32 = 32

32 + 8 + 2 = 42

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  #6  
Old April 28th, 2004, 07:29 PM
NanoWarrior NanoWarrior is offline
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Look at the table. One bit counts to two numbers, two bits count to four numbers, three bits to eight numbers, four bits to 16 numbers, five to 21, six to 64, seven to 128 and finally, one byte (8 bits) counts to 256 numbers.

Decimal Binary Representation
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

so this graph represents what each number is in binary language machine code?

And about the clock, thats a cool clock, no light represents a 0 and a light represents 1(so I suppose).

Last edited by NanoWarrior : April 28th, 2004 at 08:06 PM.

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  #7  
Old April 28th, 2004, 08:29 PM
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Quote:
Originally Posted by NanoWarrior
so this graph represents what each number is in binary language machine code?

And about the clock, thats a cool clock, no light represents a 0 and a light represents 1(so I suppose).
The graph represents what each number is in a binary number system. Its not the same as machine language. (Binary means 2 parts, in this case 0 and 1. In a computer that represents the two states of a transistor. In the counting system, it indicates which powers of two to use. You do have the idea of the counting right though)
I have that clock, it is pretty cool. You are right, on=1, off=0

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  #8  
Old April 28th, 2004, 10:07 PM
NanoWarrior NanoWarrior is offline
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Why is 2 represented as 10 though? Or 4 as 100? The only thing I don't get now is why are the decimals represented in certain binary representations, such as why is 4 represented in binary representation as 100? I read the link and other sites on how but I don't understand.

Last edited by NanoWarrior : April 28th, 2004 at 10:18 PM.

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  #9  
Old April 29th, 2004, 12:13 AM
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Code:
10-2^0(1) off
|
2^1(2) on

Code:
2^2(4)on-100-2^0 off
          |
         2^2 off

Hope this helps, I'm out of ideas how to explain it.

Last edited by karsh44 : April 29th, 2004 at 12:16 AM.

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  #10  
Old April 29th, 2004, 08:23 AM
NanoWarrior NanoWarrior is offline
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ok, thanks for the help

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  #11  
Old May 11th, 2004, 03:51 PM
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Quote:
Originally Posted by NanoWarrior
Why is 2 represented as 10 though? Or 4 as 100? The only thing I don't get now is why are the decimals represented in certain binary representations, such as why is 4 represented in binary representation as 100? I read the link and other sites on how but I don't understand.



1 | 0 | 0
2^2 | 2^1| 2^0
4 | 0 | 0 <- those are 0 because there are 0s in the binary number.

4+0+0=FOUR

my spacing got messed up, so i bet this post is of no use.

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  #12  
Old May 12th, 2004, 06:03 PM
NanoWarrior NanoWarrior is offline
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no worries I finally figured it out recently.

0 | 00000000
1 | 00000001
2 | 00000010
3 | 00000011
4 | 00000100

this is how I relized the answer to my question. Soonly it will make its way up to 255 possiblilities as 11111111.

thanks again

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  #13  
Old May 13th, 2004, 01:38 PM
streetkid streetkid is offline
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exactly, you've got it.

and 5 | 00000101

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