Hitchhiking the galaxy one last time

Did you know?

Six multiplied by nine is indeed forty-two...
...in base thirteen.

What is base 13?

In order to understand base 13, you must first consider the two most familiar bases.

The Basics

Base 10 and base 2

Base 10 is the method of calculating numbers the way that we usually do, we arrange them in to groups of 10, that is to say we have 10 digits (0-9) in this numbering system.

Base 2 (binary) has 2 digits, 0 and 1, and is different in terms of calculating numbers.

Here is how it works:

The number "1" is represented by the digit 1. When you add 1 to 1, you make 2 in base 10. However, the digit "2" is nonexistent in base 2 and so, we must add another place value to the number:

(0)1 + (0)1 = 10

So, the number "2" would be represented by "10" in binary.

Base 13 (Mark 2)

Base 13 has 13 digits. How? Well, like all of those algebra classes that we have to slave through, we're gonna be lazy and substitute missing numbers with letters!!!

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C

Two + Two = Ten?

Now, normally you would see a lot of references to the question "What is 2 + 2?" in pop culture. Usually, the following answer seems to be a completely random number (or word lol) that we find absurd, say 10. With all that you have learned in the past 2 minutes, you know of course that bases allow for seemingly "weird" answers. That is the case here, in which GLaDOS recites in "Portal" after you incinerate her curiosity module:

"Two plus two is... [static] ...ten............in base four! I'm fine!"

I sense that you are puzzled, let's try this question and start from the basics:

Base 4 has 4 digits: o, 1, 2, and 3

2 + 2 is the same here as in base 10 but it would help if you add a zero before it:

(0)2 + (0)2 = _____

There is no digit here that represents 4, so we will have to add a place value...

(0)2 + (0)2 = 10

So... there you go.

Multiplying..........................................................in base four!

I'm not going to explain thoroughly on this one, but try to follow along... ok?

Let's try 2 x 3

(0)2 x (0)3 =
(0)3 + (0)3 = (0)6

There is no 6, so we'll convert. Let's look at the next 3 numbers:

(0)3, 10, 11, 12

so:
(0)2 x (0)3 = 12 (6)

Base 16

Base 16, (aka hexadecimal) is commonly used in games. It basically ranges from 01 to FF in value and determine an attribute in the game (characters, objects, etc.). For example, 01 might be Player 1, 02 would be Player 2, 03 is a cleverly hidden easter egg that was originally intended to be a joke by the programmers to completely screw up the game should someone hack it by messing with Gameshark... and so on. Glitches often occur when the hex value does not match actual data from the game, causing a abnormality that is often deadly to a game (see "missingno." on Wikipedia)

Conclusion:


I am NOT going to calculate 6 x 9 in base 13.
Good Day

This was a triumph!
I'm making a note here:
"HUGE SUCCESS!!"

It's hard to overstate
my satisfaction.

Aperture Science;
We do what we must,
because we can.

For the good of all of us.
Except the ones who are dead.

But there's no sense crying
over every mistake.
You just keep on trying
till you run out of cake.
And the science gets done,
and you make a neat gun
for the people who are
still alive.

I'm not even angry...
I'm being so sincere right now -
Even though you broke my heart,
and killed me.

And tore me to pieces.
And threw every piece into a fire.
As they burned it hurt because
I was so happy for you!

Now, these points of data
make a beautiful line.
And we're out of BETA.
We're releasing on time!
So I'm GLaD I got burned -
Think of all the things we learned -
for the people who are
still alive.

(Go ahead and leave me...)
(I think I'd prefer to stay inside...)
(Maybe you'll find someone else
to help you?)
Maybe Black Mesa?
That was a joke! HAHA!! FAT CHANCE!!

Anyway this cake is great!
It's so delicious and moist!

Look at me; still talking
when there's science to do!
When I look out there,
it makes me GLaD I'm not you.

I've experiments to run.
There is research to be done,
on the people who are
still alive.
And believe me I am
still alive.
I'm doing science and I'm
still alive.
I feel fantastic and I'm
still alive.
While you're dying I'll be
still alive.
And when you're dead I will be
still alive.

Still alive.

Still alive.