A look into math part one. All Your Base.

Earlier today,(by day I mean any time in the past 7 days) I was writing out the Fibonacci numbers and thought “could I make a base Fibonacci?”

Well before we answer this question we need to know two things; what is a base and, what are the Fibonacci numbers.

In this post we will cover the harder one; what is a base?
Well according to dictionary.com a base is “the bottom support of anything; that on which a thing stands or rests: a metal base for the table.” Wait… sorry… here

13.
Mathematics.
a.
the number that serves as a starting point for a logarithmic or other numerical system.
b.
a collection of subsets of a topological space having the property that every open set in the given topology can be written as the union of sets of the collection.
c.
a collection of neighborhoods of a point such that every neighborhood of the point contains one from the collection.
d.
a collection of sets of a given filter such that every set in the filter is contained in some set in the collection.

Let us pull that apart and make some more sense of it.

In our day to day life we come across three bases, what we work in base 10 (Dec), what is used in making colors for computers base 16 (Hex), and the life blood of computers base 2 (bin)

We will start with what we all know, base 10.
At every power of 10 we add a place. What do I mean by that?
Well the powers are 1, 10, 100, 1000… (10^0, 10^1, 10^2, 10^3…)
With a base 10 we need 10 deferent symbols we use 0,1,2,3,4,5,6,7,8,9.
So how does this work in real life? Well lets take the number 1138 why well I like that number.
We have one 10^3 (A.K.A. 1000) one 10^2 (A.K.A 100) three 10^2 (A.K.A 30) and eight 10^0 (A.K.A 8). So we have 1000+100+30+8 = 1138 at this point may be thinking well Duhh T100 we know 1138=1138 but stay with me.

We will now look at the number 18C6 WAIT!!!!!!!! “C” is not a number! But it is in base 16 known as Hexadecimal (Hex). We now need 16 symbols to use so we will use 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F. So the points that we need add a new place is at the powers of 16 they are , 1, 16 , 256, 4096…(16^0, 16^1, 16^2, 16^3…)(all these numbers are in Dec for the readers)

So lets get back to our number 18C6
We have one 16^3 (A.K.A. 4096 in Dec) eight 16^2 (A.K.A. 2048 in De) twelve 16^1 (A.K.A. 192 in Dec) and six 16^0 (A.K.A. 6 in Dec) So we have in Hex 1000 + 800 +C0 +6 = 18C6 In Dec this would be 4096 + 2048 +192 +6 = 6342
Hex is used for colors in computers. The color is made by the mix of red green and blue (RBG) ranging FFF,FFF,FFF (black) to 000,000,000 (white)

roses are _#FF0000 violets are _#0000FF all my base are belong to you. =P

Now on to the best base of all base 2 (bin)
So by now you know the drill. Being only base 2 we only need 2 we will use 0,1.
The powers are:; 1,2,4,8,16,32,64,128,256…(2^0, 2^1, 2^2, 2^3, 2^4, 2^5, 2^6, 2^7, 2^8…). Lets take this number 101010. We have a one in the 32 space (2^5), nothing in the 16 space (2^4), a one in the 8 space (2^3), nothing in the 4 space (2^2), a one in the 2 space (2^1), and last nothing in the 1 space (2^0). We not have 32+0+8+0+2+0=42.
Now why would we ever use this? It takes more space then any other base (save base one, but we got away form tick marks a long time back). Well it only needs to states on or off (0 or 1) this can be done with a normal switch or one variable. It allows us to change logic tables into an electric form if you have three switches; A, B, and C, and you want to know what state they are in you can do so with one number. If A is on B is off and C is on, we get 101 or in Dec this would be 5 (we have one in the 1 place nun in the 2 place and one in the 4 place 1+0+4 =5). So you can set three switches with one number lets say we want A off B on and C off all we need is 2 (the computer takes it and changes it to 010 A is off (0) well B is on (1) and C is off (0)).

I hope this has help and not just mixed you up more. Fell free to post ether way.
“See” you next week.
T100