Beginners guide to Decimal-Binary Numbering...
Understanding DECIMAL & BINARY Numbering .....
DECIMAL :Decimal system rates everything as a value of 1.
The more 1's you can count, the higher the count.
Look down at your hand, and count FIVE fingers.
The maximum you can count to is only 5.
This is simply because each individual finger only has a value of "1"
To count higher, obviously you need more fingers, Count the fingers of both hands and now you can count to "10".
BINARY :Binary system values everything as either a 0 or a 1.
The various patterns of 0's and 1's provide the value that is being counted.
Example :
Binary uses a "doubling system" for the values of each finger.
So, Let's assign permanent values to your fingers :
Thumb=16, Index finger=8, Middle finger=4, Ring finger=2, Little finger=1
See how each finger is simply DOUBLE the value of the finger to it's right?
The fingers NEVER change their value, but they are simply turned OFF (0) or turned ON (1)
Binary only has 2 possible states, 0 or 1 (also known as OFF or ON)
In this example, Lets assume an extended (straight) finger is a "1" and a curled up (hidden) finger is a "0"
Holding out your fist, this would represent "0" as all fingers are hidden. (all 0's - All OFF).
Now extend your "little" finger, this is a "1"
Hide your "little" finger and extend your "ring" finger, this is a "2"
Hide your "ring" finger and extend your "middle" finger, this is a "4"
Ok, so HOW do we get a 3 or 5, 6 or 7 etc ????
Now extend your "little" finger AND your "ring" finger, this is now a "3" because your little finger (1) ADDED to your "ring" finger (2) = 3.
Close your fist, and try this...
Now extend your "little" finger AND your "middle" finger, this is now a "5" because your little finger (1) ADDED to your "middle" finger (4) = 5.
Close your fist, and try this...
Now extend your "little" finger AND your "ring" finger AND you "middle" finger, this is now a "7" because your little finger (1) ADDED to your "ring" finger(2) ADDED to your "middle" finger (4) = 7.
Let's go all out, and extend all 5 fingers, this will equate to "32" when we add all the fingers together.
"little" finger (1),
ADDED to :
"ring" finger (2),
ADDED to :
"middle" finger (4),
ADDED to :
"index" finger (8),
ADDED to :
"thumb" (16),
1+2+4+8+16 = 32.
How's that? you can count upto 32 on one hand now, instead of a measly "5"
Ok, Let's go mental, and use 2 hands now....
Assuming the fingers on your RIGHT hand are valued as 1,2,4,8,16 and your LEFT hand will continue doubling values as 32,64,128,256, 512.
By extending ALL 10 fingers (this would be the binary of "1111111111" (10bits) we now get :
1+2+4+8+16+32+64+128+256+512 = 1024.
YEP ! with only 10 fingers, you can now count upto "1,024" instead of "10".
...you'd look silly with 1,024 fingers anyway.
I usually show this system in person, and/or write it out on paper to illustrate the "values" of each digit (finger) when counting with binary numbers.
Hope this clears up some basic binary skills.
MM.
