LearnTronics
Logic Before Electronics
Logic before logic gates
Before we draw an AND gate or talk about ones and zeros, it helps to understand what logic is doing in ordinary language.
Start with a statement
A statement (often called a proposition) is a sentence that makes a claim which can be considered true or false.
“The lamp is on.” is a statement. “Is the lamp on?” is a question. “Turn the lamp on.” is a command. Logic treats those differently.
Premises and conclusions
An argument begins with one or more premises and asks what conclusion follows from them.
Socrates is a person.
Therefore, Socrates is mortal.
The important point is the form: if the premises are true, the conclusion must follow.
Another way to think of this
An electrician troubleshoots this way all the time:
“If the supply is present, the fuse is good, the switch is closed, the wiring is intact, and the lamp is good, then the lamp should light.”
That is already a logical statement built from several conditions. Later we will turn those words into switches and then into logic gates.
Truth is not the same thing as validity
A premise can be wrong even when the form of an argument is valid. Logic tells us what follows if the premises are accepted. It does not magically guarantee that the premises describe the real world correctly.
As programmers often say: “Garbage in — garbage out.” Perfect reasoning applied to bad starting information can still produce a useless result.
A little history
People were reasoning, arguing, and trying to describe good reasoning long before Aristotle. Earlier Greek thinkers had already examined argument, proof, contradiction, and methods of debate.
Aristotle (384–322 BC), however, is generally credited with giving deductive reasoning its first systematic formal treatment. His study of the syllogism showed that an argument could be judged by its form: certain conclusions follow necessarily when the premises have the proper relationship. His logical works became the foundation for the formal study of logic for many centuries.
Try these yourself
A little deeper
In modern symbolic logic, a simple statement is often represented by a letter such as A or B. Instead of repeatedly writing “the motor is running,” we can simply let A mean “the motor is running.” Then we can study how statements combine without being distracted by the subject matter.