What is Combinational Logic?

The most important thing to know is that a combinational logic circuit's output depends only on its current inputs. It has no memory of what happened in the past. You put in some 1s and 0s, and you get an output of 1s and 0s based on a fixed rule.

The Fundamental Building Blocks and Rules

1. Transistors, the fundamental building block

• At the very bottom, all digital computers are built from tiny electronic switches called transistors. (we won’t go further down than here in this course)
• It’s helpful to think of a transistor as a simple on/off(1/0) switch controlled by electricity. Depending on the input to its "Gate," it either lets electricity flow or it doesn't.

2. Logic Gates

• We combine a few transistors to create basic logic gates like AND, OR, and NOT. These are the fundamental units we’ll work with.
  • AND: Output is 1 only if all inputs are 1.
  • OR: Output is 1 if any input is 1.
  • NOT (or Inverter): Flips the input. 1 becomes 0, 0 becomes 1.

3. Boolean Algebra as the language

• Boolean Algebra is the math used to describe what these circuits do using 1s and 0s.
• AND is written like multiplication (A⋅B).
• OR is written like addition (A+B).
• Using the rules of this algebra, you can manipulate equations to simplify your logic circuits, making them smaller and faster. This is a critical design choice based on the goal of building a computer chip.

A Universal Recipe for Building Any Circuit

How do you go from an idea to an actual circuit? There's a standard method called Sum of Products (SOP).

1. List all possibilities by creating a "truth table" that shows what the output should be for every single combination of inputs.
2. Focus only on the rows where the output is 1.