1: Logic & Instances

We start with the fundamentals of logic gates and logical expressions using De Morgan's Law. By looking at transistors, the most granular aspect of CS, we can steadily add layers of abstraction.

Learning Targets

• I can explain the connection between electricity and logic.

• I can interpret logical statements with all common operators, (i.e. and, or, nor, xor, if, iff).

• I can simplify a logical expression according to De Morgan's Laws.

• I can convert numbers from decimal to binary and to hexadecimal.

• I can describe the purpose of instantiation.

• I can decide when to instantiate an object or when to use a static class.

Logic Gates

I'm absolutely fascinated in how people build logic, systems that react to conditions, into physical devices.

We start with two tricks with circuits: 1) and && 2) or ||

With tiny transistors and these building blocks, we can assemble our modern technological era. Let's just take a peak:

De Morgan's Law

You'll need to know how to distribute the ! when simplifying logical expressions. This will make more sense as we get into more practical examples.

De Morgan's Laws essentially describes the distributive property of "not" or !

A "promise" or an "if" within logic is something like:

It's only false if the condition was met (you studied) but you did not get the promised result.

iff means they both have to be the same for <-> to be true

Practicing Boolean Logic

Let's simplify these statements. Reduce them down to just true or false

• true != true || (true || false)

• false && true || true && false || true && false || true

• !(true && false)

• !(5 > 5)

• !(5 <= 5)

• 5 == 5 && true

Binary

Can you see how false and true could also be considered to be 0 and 1? All the sudden, we can make these logic gates, these electrical transistors, store binary data. Computers are pretty cool.

Instantiation

This is an important concept that's most easily introduced when we're not thinking about the code. If you have a recipe to make a cake, that's similar to a class definition. Each time you bake a cake, you're creating a new instance of that cake.

One cake recipe produced many objects

A whiteboard has functions but is not replicable. It's a static resource

Another example of instance VS static classes

This is by no means a perfect example as things are more complicated... but let's consider Fortnite for a moment. There's just one map. Programmers might refer to this map by its class. If I wanted to call a tornado, at Coney Crossroads, I might type something like, Map.createTornado("Coney Crossroads");

One map and globally accessible resources. An potential example of a static class

Now let's imagine a programmer wanted to provide a player with some individual powers. I wouldn't want to be so broad as to call the whole Player class as each player is an individual. I'd want to specify which individual player, something like lancerGuy99.upgradeWeapon();

Each person controls an instance of the Player class. Each copy of stores the user's skin, current health, etc.