So you live in this world where there are
only 1's and 0's, like you have no pencils
and only Cherrios and twigs to keep
track of your counting ways.
So you say, okay, I'm going to count in units of base 2.
This works because any even number can be expressed
as a multiple of 2, and any odd number can be thought
of as a multiple of 2 with a +1 thrown in at the end.
So, instead of our normal world of base tens
place values
103 102 101 100
1,000 100 10 1
thousands hundreds tens ones
We have this place value world:
26 25 24 23 22 21 20
64 32 16 8 4 2 1
So, if we have the binary number:
“10”
It’s really
(1 x 21) + (0 x 20)
or (1 x 2) + (0 x 1)
or (2) + (0)= 2
Another example:
The number “11011”.
If we use our place value cheat sheet:
24 23 22 21 20
16 8 4 2 1
and put our 1 1 0 1 1
binary number
in the right places
You can think of it as a shopping list;
I have one 24, one 23, no 22, one 21, and one 20.
We have:
(1x16)+(1x8)+(0x4)+(1x2)+(1x1)=
16+8+2+1=27
so “11011” = 27 in our every day decimal, base 10 world.
Binary mathematics is a world of haves and have nots,
yes or no, black and white. It's either 1 (yes) or 0 (no).
I either "have" that muliple of two in my desired number,
or I don't. It may not be as neat and nifty as our normal
0-9 world, but it is a fun way to while away the hours in
a doctor’s office.