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ProPoSitioNal logic, Hardware

imPlemeNtatioN, aritHmetic

oPeratioNS

3

Learning Objectives

3.1 Propositional Logic 3.2 Well-Formed Formulas and Truth Values
3.3 Connectives 3.4 Converse, Inverse and Contrapositive
3.5 Equivalence Propositional Laws 3.6 Tautology, Contradiction and Contingency
3.7 Logic Gates 3.8 Half Adder and Full Adder

Logic is the subject that deals with valid reasoning leading to inference. According to Aristotle, “logic is new and
necessary reasoning”. It is said to be 'new' because it lets us know the unknown and ‘necessary’ as it leads to important
conclusions. Logical reasoning is the fundamental base of some branches of Mathematics and Computer Science.
Logic may be informal, formal, symbolic or mathematical.
Symbolic logic represents logical expressions using symbols or variables instead of language statements. Logical
expressions are the statements that can either be true or false. An interrogative statement like “Why are plants green?”
or an imperative statement like “Do your homework” or an exclamatory statement like “What a shot!”, are not logical
statements. But a declarative statement like “Rohan is the best goalkeeper” can either be true or false or in other
words, it has a truth value. The statements that produce only true or false as answers are called propositions. They are
the building blocks of logic.

Let us examine some statements:
Statements Type
The month of May is very hot. It is a proposition as the answer can be true or false. [mostly true]
Disha hates vegetables. It is a proposition because the answer can be yes or no.
Good morning! It is not a proposition as commands or wishes cannot be true or false.
What are you reading? It is not a proposition as such questions cannot be true or false.

3.1 PROPOSITIONAL LOGIC
Propositional logic is a branch of symbolic logic that deals with propositions and how each proposition relates to
one another. It studies the methods of combining or modifying propositions to form more complex propositions.
A proposition is represented by propositional variables containing a single letter generally written in lowercase.

Definition

A proposition is a declarative statement which can either be true or false, but not both or any other value.

Propositional Logic, Hardware Implementation, Arithmetic Operations 67