Page 99 - Bebop to The Boolean Boogie An Unconventional Guide to Electronics Fundamentals, Components, and Processes
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Boolean Algebra
One of the most significant mathematical tools available to electronics
designers was actually invented for quite a different purpose. Around the
1850s, a British mathematician, George Boole (1815-1864), developed a new
form of mathematics that is now known as Boolean Algebra. Boole’s intention
was to use mathematical techniques to represent and rigorously test logical and
philosophical arguments. His work was based on the following: a statement is a
sentence that asserts or denies an attribute about an object or group of objects:
1 Statement: Your face resembles a cabbage.
Depending on how carefully you choose your friends, they may
either agree or disagree with the sentiment expressed; therefore,
this statement cannot be proved to be either true or false.
By comparison, a proposition is a statement that is either true or false with
no ambiguity:
Proposition: I just tipped a bucket of burning oil into your lap.
This proposition may be true or it may be false, but it is definitely
one or the other and there is no ambiguity about it.
Propositions can be combined together in several ways; a proposition
combined with an AND operator is known as a conjunction:
