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Boolean Expression Simplification and Circuit Development Guide

Learn how to simplify boolean expressions and develop circuits, with examples and rules for effective implementation. Dive into the world of circuits, Boolean expressions, and truth tables.

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Boolean Expression Simplification and Circuit Development Guide

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  1. Circuits & Boolean Expressions

  2. Boolean Expression: X = A B C + A B C Simplify the Expression: X = A B C + A B C B C ( A + A ) B C ( 1 ) B C A ABC ABC+ABC Example # 1: Develop a circuit and truth table from a Boolean expression ABC BC BC Unsimplified Circuit

  3. Example # 1: Unsimplified X = A B C + A B C __ A B C X 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 A B C X 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 _ A B C Example # 1: Simplified X = B C A B C

  4. Example # 2 Boolean Expression: X = A B C + C Simplified: X = A B + C Rule: AB + C = A + C Develop a truth table and Boolean Expression from a circuit: A A AB B ABC C C

  5. Example # 3: Boolean Expression: X = A B C + A B C + A B C Simplify: A B ( C + C ) + A B C A B + A B C 1 A AB AB +ABC B AB ABC Develop a logic circuit and Boolean expression from a truth table A B C X 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0

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