| OOOOOPPPPPPSSSSSS !!!!
Thats the way it goes when you are doing something a little to fast.
How about this
2^1 = 2
2^2 = 2*2 = 4
2^3 = 2*2*2 = 8
2^4 = 2*2*2*2 = 16
2^5 = 2*2*2*2*2 = 32
2^6 = 2*2*2*2*2*2 = 64
2^7 = 2*2*2*2*2*2*2 = 128
2^8 = 2*2*2*2*2*2*2*2 = 256
2^9 = 2*2*2*2*2*2*2*2*2 = 512
2^10= 2*2*2*2*2*2*2*2*2*2 = 1024
2^11= 2*2*2*2*2*2*2*2*2*2*2 = 2048
2^12= 2*2*2*2*2*2*2*2*2*2*2*2 = 4096
2^13= 2*2*2*2*2*2*2*2*2*2*2*2*2 = 8192
2^14= 2*2*2*2*2*2*2*2*2*2*2*2*2*2 = 16384
2^15= 2*2*2*2*2*2*2*2*2*2*2*2*2*2*2 = 32768
2^16= 2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2 = 65536
and some more :
2^0 = 1
2^-1 = 1/2 = 0.5
2^-2 = 1/(2*2) = 0.25
2^-3 = 1/(2*2*2) = 0.125
2^-4 = 1/(2*2*2*2) = 0,0625
The importance of this is that computers and other digital systems uses
a binary numbers system in which every number is represented by a number
of "bits" which can have a value of 0 or 1.
This is called a number system with a base of 2.
The wordlength is how many bits you are using.
For example with a wordlenght of 3 you count like this
000 = 0
001 = 1
010 = 2
011 = 3
100 = 4
101 = 5
110 = 6
111 = 7
With a wordlenght of 3 you can count 8 numbers
2^3=8
Similar with a wordlenght of 8 you can count 2^8 = 256 numbers
and with a wordlenght of 16 you can count 2^16 = 65536 numbers
Computers usually use wordlenghts of 8,16,32 or 64
Note this wordlenghts are itselfs a power of 2 which
shortly explained makes it more efficient for the computer
to store and fetch the numbers
Generally speaking one can say:
- computers really like things that are a power of 2
- people that programs to much assembly or makes digital electronics
starts dreaming binary and hexadecimal numbers
Hexadecimal numbers by the way are a numbers system with a base of 16 instead of
10 which is our normal number system and is called decimal number system
Hex Dec Bin
0 = 0 = 0000
1 = 1 = 0001
2 = 2 = 0010
3 = 3 = 0011
4 = 4 = 0100
5 = 5 = 0101
6 = 6 = 0110
7 = 7 = 0111
8 = 8 = 1000
9 = 9 = 1001
A = 10 = 1010
B = 11 = 1011
C = 12 = 1100
D = 13 = 1101
E = 14 = 1110
F = 15 = 1111
Roger K
"David O. Baird" wrote:
>
> Sonicman,
>
> I though you might want to know that Roger Klaveness's response to your
> question contained a typographical error that resulted in incorrect
> definitions of 2^7, 2^8 and 2^9. His response should have been:
>
> 2^1 = 2
> 2^2 = 2*2 = 4
> 2^3 = 2*2*2 = 8
> 2^4 = 2*2*2*2 = 16
> 2^5 = 2*2*2*2*2 = 32
> 2^6= 2*2*2*2*2*2 = 64
> 2^7= 2*2*2*2*2*2*2 = 128
> 2^8= 2*2*2*2*2*2*2*2 = 512
> 2^9= 2*2*2*2*2*2*2*2*2 = 1024
> |