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Boolean algebra and Shannon's circuit analysis | Math Foundations 260 | N J Wildberger
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The development of circuit analysis in the 20th century had strong connections to the theory of logic. In this video we discuss Huntington's general formulation of Boolean algebra as an abstract theory, and then investigate Claude Shannon's important 1938 paper which first lays out the connections between Boolean algebra and circuit analysis.
There are some surprises here, as Shannon's initial orientation was in some sense opposite to the modern point of view --- he sees the logical laws as applying to what he calls "hindrances" to flow in circuits. Nevertheless he shows that Huntington's Boolean algebra with its many interesting reduction formulas was well suited to simplify, and more generally understand, complicated circuits.
Unfortunately he appears not to have read the original paper of Boole; and this ends up affecting the development of electrical engineering in the 20th century.
Video Content:
00:00 Introduction
2:42 Edward Huntington 1904
7:41 Claude Shannon
11:24 Series and parallel
16:13 Shannon's example
20:42 Reduction rules in Boolean algebra
23:10 Exercises
Here are the Insights into Mathematics Playlists:
Here are the Wild Egg Maths Playlists (some available only to Members!)
************************
There are some surprises here, as Shannon's initial orientation was in some sense opposite to the modern point of view --- he sees the logical laws as applying to what he calls "hindrances" to flow in circuits. Nevertheless he shows that Huntington's Boolean algebra with its many interesting reduction formulas was well suited to simplify, and more generally understand, complicated circuits.
Unfortunately he appears not to have read the original paper of Boole; and this ends up affecting the development of electrical engineering in the 20th century.
Video Content:
00:00 Introduction
2:42 Edward Huntington 1904
7:41 Claude Shannon
11:24 Series and parallel
16:13 Shannon's example
20:42 Reduction rules in Boolean algebra
23:10 Exercises
Here are the Insights into Mathematics Playlists:
Here are the Wild Egg Maths Playlists (some available only to Members!)
************************
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