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4.1 : An Overview
Some History
While you will never need to know this for an exam, it's important to know the origins of boolean algebra. Boolean algebra was named for George Boole. George Boole is a man who is long dead now that has lots of impacts on the field of computing. He wrote a fancy paper called An Investigation into the Laws of Thought. To summarize, the paper focused on how the brain uses a series of true and false statements in combination to make decisions. Boolean algebra is the computation of these combinations of statements.
In English
Before we start doing boolean algebra, we should probably start with learning about basic boolean expressions. A boolean statement is a statement that is either true or false. "It is raining today" is a good example. If it is raining, the statement is true. If it is not raining, the statement is false. Computers really like boolean statements. If we recall, computers evaluate binary. Binary has only two values, 0 and 1. Booleans also only have two values, false and true. This means we can really think of two states, On and Off, True and False, 1 and 0. This means 0, false and off all correspond to the same state while 1, true and on all correspond to the same state.
In Math
While boolean algebra started as a thought process, there are a lot of applications. The applications we focus on in computer science are mathematical. This includes basic algebra, set theory and circuits. This guide will mostly focus on circuits. However, I will talk about other applications where applicable.
Practice Problems
Evaluate this boolean statement. Seven is an odd number.
Evaluate this boolean statement. B is the first letter of the alphabet.