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Digital Electronics

A digital circuit is constructed from logic gates. Each logic gate performs a function of boolean logic based on its inputs, such as AND or OR. Each circuit can be represented as a Boolean Algebra expression; this topic is an extension of the topic of Boolean Algebra, which includes a thorough description of truth tables and simplifying expressions.

Definitions

The following table illustrates all logic gates. For each logic gate, the table shows the equivalent Boolean algebra expression and truth table. image.pngimage.png

Online Tools

The Logisim application is a wonderful tool for exploring this topic. Logisim is free to download and use; among its many features is support to automatically draw a circuit from a Boolean Algebra expression; to simulate the circuit with arbitrary inputs; and to complete a truth table for the circuit. From the application, you can import the circuit corresponding to the Sample Problem 1 from the file located at http://www.acsl.org/misc/wiki-digital-electronics-sample1.circ

Sample Problems

Digital Electronics

Find all ordered triplets (A, B, C) which make the following circuit FALSE:

NotABorC.svg

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Digital Electronics

How many ordered 4-tuples (A, B, C, D) make the following circuit TRUE?

Circuit-sample2.svg

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Digital Electronics

Simplify the Boolean expression that this circuit represents.

Circuit-PB.png

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