by **Magic88889** » Sun Mar 05, 2017 11:29 pm

Crash course on base 4 math, here we go! I hope it makes sense.

First, we'll look at how we write values in base 10, our normal number system. Say we want to write the value twenty-three:

Since the number is greater than ten, in the base ten system, we'll need more digits. In this case 2 digits.

For the tens digit, value is equal to 10 times the value of the number. In this case, we put 2. So 2x10=20.

Then the ones digit is 1 times the value of the number. In this case, we put three, so the value of the ones digit is 1x3=3.

For any number the number you multiply by to get the value is 10^n, where n is the number of the digit minus one.

So for the 100s digit (or the third digit), value would get times 10^(3-1) = 10^2 = 100.

We then add the values of the digits together to get 23.

A base 4 system works the same way. Let's work with the same number. Note that there are only 4 values that can be in each digit (that's the meaning of base 4). For this, we'll use 0,1,2,3.

Because we have a base 4 system, the former tens digit is the fours digit (or whatever you want to call it, although I'm sure there is a proper name).

However, since we can only get to 15 with 2 digits we need another one.

So, starting with the third digit. Using the same rule as above the value will be multiplied by 4^(3-1) = 4^2 = 16. So maybe this can be the sixteens digit.

We only need one value on this digit, because 2*16 is too high. So the first digit is 1.

The next digit will be multiplied by 4, because 4^(2-1) = 4^1 = 4. Putting a one in this digit will bring us to overall value of twenty, so that's all we need.

Number is now 11?.

We need three more to equal our goal. Fortunately, the final digit is multiplied but 1, because 4^(1-1) = 4^0 = 1. So we can just put a 3 there and we're good to go.

So in the end, twenty-three written in base 4 looks like this: 113. Because that's (1x16)+(1x4)+(3x1)=16+4+3=23.

I hope that made sense, although I'm sure there's plenty of resources out there to help with that.

Now the panels work exactly like that. Each digit is represented in a different area of the panel, with a maximum of five digits. First digit it right in the center. If you use the number simulator in the garage, you can see each value for the ones digit: 0,1,2, and 3. Zeros are blank. Ones look like this: \ Twos look like < and threes look like y (sort of). For the first (or ones digit) everything is centered on the center dot. To get the next digit (the fours digit), you just move the whole thing up one dot. So the same three shapes give you the same values for the digit. Then we just more clockwise around the panel. The sixteens digit in reached by moving to the right. The sixty-fours digit by moving down, and the final digit (the two-hundred-fifty-sixs digit?) is reached by moving left from the center dot.

So the bridges each have five parts to them, each with 4 settings. Each part is controlled by a digit. The first digit controller the first part, the second digit controls the second part, ect. The 4 settings are 0 (off), 1 (framework only), 2 (blue solid surface), and 3 (fully formed). A setting of 2 or 3 works perfectly. So to form a bridge, you only need to write a two or three in each digit. A fully formed bridge would have the value of 33333, or 1023 in base 10.

....I hope I didn't just confuse you more.