Solving Boolean Logic Expressions with And, Or and Not Gates

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SUMMARY

This discussion focuses on solving Boolean logic expressions using AND, OR, and NOT gates with two Boolean variables, A and B. The three expressions analyzed are: Expression 1: (A and (not B)) or (B and (not A)), Expression 2: (A and (not B)) and (B and (not A)), and Expression 3: (A or B) and (not ((A and B))). The key conclusion is that Expression 1 and Expression 3 are identical in output for all combinations of A and B, while Expression 2 differs. Constructing truth tables is recommended for clarity in determining the equivalence of these expressions.

PREREQUISITES
  • Understanding of Boolean algebra
  • Familiarity with logic gates: AND, OR, NOT
  • Ability to construct truth tables
  • Basic knowledge of Boolean variables
NEXT STEPS
  • Learn how to construct truth tables for complex Boolean expressions
  • Explore Boolean algebra simplification techniques
  • Study the properties of logic gates and their combinations
  • Investigate the use of simulators for digital logic design
USEFUL FOR

This discussion is beneficial for students studying digital logic design, educators teaching Boolean algebra, and anyone involved in computer science or electrical engineering who needs to understand logic gate operations.

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The three equations below represent three different logic expressions using and, or and not gates of two boolean variables A and B. A boolean variable can take only one of two possible values: True or False.

Which of the two expressions are identical, meaning that for any combination of A and B they are both True or both False.

Expression 1: (A and (not B) ) or ( B and (not A))
Expression 2: (A and (not B)) and ( B and ( not A ))
Expression 3: (A or B ) and ( not ((A and B ))

In your answer explain how you figure out which expression is different (in terms of its output given the same combination of A, B and C) from the other two.

I tried to use the simulator to construct these, but since we don't have any combination gates on our program (NOR, NAND, etc.), I'm having a lot of trouble with it. We only have the AND, OR, and NOT gates to work with. Could someone please help me? I am really confused right now. Thank you.
 
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Expect it to be moved soon.

That aside, you could just construct truth tables and see which end up the same.

Or are you supposed to use boolean algebra to turn one of them into another?
 
I actually just figured this one out. Thank you for the pointer, though!
 

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