Why do Boolean functions play a central role in hardware architectures?

The heading as you see it is exactly the question raised by my CS1104 — Computer Systems instructor for my discussion assignment. In case you do not have a CS degree or never took a course dubbed “computer systems” in college, or anything remotely close to it, it might be worthwhile explaining the key terms for you: boolean functions and hardware architecture, even though you can just ask ChatGPT😀

Boolean functions

In the language of mathematics and computing, boolean functions are simply binary functions. They take input values that can ONLY be either true or false, often represented by the binary values 1 and O, respectively.

Boolean functions can have one or more input variables and produce a single output based on the logical operations performed on the inputs. The basic operations in Boolean algebra include AND, OR, NOT, XOR (exclusive OR), and NAND (NOT AND), among others.

The father of Boolean algebra, George Boole (1815–1864)

Let’s imagine you’re in the kitchen preparing a recipe, and you have a set of ingredients that can either be present (true) or absent (false). Each ingredient represents a binary variable. Now, let’s define some Boolean operations using this cooking scenario:

AND Operation (Conjunction):

• Scenario: Making a sandwich with…