Saturday, April 3, 2010

Binary Digits.

Consider the number 783 which can be obtained by:
7 x 102=700
8 x 101= 80
3 x 100= 3
78310 Total= 78310

In the decimal system, we are counting how many 10s, 100s, 1000s, 10000s etc. there are. Then we are multiplying the number depending on where it is positioned, and finally, we add them up.

If we were to do the same to the 8th base, then the above table will look as follows:

1 x 83=512
4 x 82=216
6 x 81=48
7 x 80=7
14678 Total= 78310

Now the number 78310 ~= 14678. This means that any number (like 783) can be written to any number base; even its own. So in computers we are interested in binary digits, as the switches in circuits are either ON or OFF. With this in mind, the number above (783) would be written in binary form as follows:


1 x 29=512
1 x 28=256
0 x27=0
0 x 26=0
0 x 25=0
0 x 24=0
1 x23=8
1 x22=4
1 x21=2
1 x 20=1
11000011112 Total= 78310


This means that:
11000011112 ~=78310

Here is a sequence that may simplify this process a bit better:

20 = 1 = 12
21 = 2 = 102
22 = 4 = 1002
23 = 8 = 10002
24 = 16 = 100002
25 = 32 = 1000002
26 = 64 = 10000002
24 = 128 = 100000002
and so on...

So now, gifting somebody $32.00 in decimal form will be written in binary as $100,0002 and giving $64.00 = $1,000,0002 which is a LOT OF MONEY... :).

As the joke goes: There are 10 kinds of people, the kind that understand binary numbers and those who do not.