Well, let me see if I can explain this. I understand the concept...
Important things to know:
* Anything to the power of 0 equals 1.
* Writing in the decimal (base 10) system is a shorthand just like binary (base 2) system is.
* The number 0 is always included in the count (which is why binary only has 1 and 0 and decimal is between 0 and 9) this is explained later.
So, we have "base 10" number system. i.e. you could write:
10^0 = 1
10^1 = 10
10^2 = 100
etc...
This is the way the number system works... essentially write the number 100 is shorthand for writing that you have:
0(10^0) = 0
0(10^1) = 0
1(10^2) = 100
i.e. you have 0 10's to the power of 0 (1's place); you have 0 10's to the power of 1 (10's place); lastly, you have 1 10 to the power of 2 (100's place). Another example:
253 is shorthand for writing:
3(10^0) = 3
5(10^1) = 50
2(10^2) = 200
then add it all together... and you have 253 OR 2 Ten to the second powers, 5 ten to the first powers, and 3 ten to the zero powers.
Now that's easy right? Just remember that it can only go from 0 to 9 because that is 10 numbers total... i.e. 0,1,2,3,4,5,6,7,8,9 is ten numbers because you count the zero. Now, let's check out a different base... base 2.
So, we all know binary, right? 010... so what the heck does that mean? Well, let's convert it to base 10.
Remember how base 10 worked? It's the same for base 2...
2^0 = 1
2^1 = 2
2^2 = 4
etc...
010 means... (left to right first)
2nd
.....0...............1................0
..../ \............./ \............../ \
....\ /.............\ /..............\ /
....2^2...........2^1............2^0
(from right to left now)
0(2^0) = 0
1(2^1) = 2
0(2^2) = 0
Add it all together and you get 2. I.e. 010 in binary = 2 in base ten (decimal system).
Can you figure out what the binary string 111 equals?
1(2^0) = ?
1(2^1) = ?
1(2^2) = ?
add it all together and you get?
