Solving Boolean Logic Expressions with And, Or and Not Gates

In summary, the three logic expressions using and, or, and not gates of two boolean variables A and B were given. The task was to determine which two expressions were identical in terms of their output for any combination of A and B. The first and third expressions were found to be identical, while the second expression was different. This was determined by constructing truth tables or using boolean algebra to show that the first and third expressions had the same output for all combinations of A and B, while the second expression had different outputs.
  • #1
intellect
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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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  • #2
Homework questions need to be in this forum:

Science Education > Homework & Coursework Questions > Engineering, Comp Sci, & Technology

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?
 
  • #3
I actually just figured this one out. Thank you for the pointer, though!
 

1. What is Boolean logic?

Boolean logic is a type of algebraic logic that uses the operators "and", "or", and "not" to evaluate the truth values of logical statements. It is commonly used in computer programming and electrical engineering to make decisions based on the outcome of logical expressions.

2. What are the basic Boolean logic gates?

The basic Boolean logic gates are the AND gate, the OR gate, and the NOT gate. These gates are used to manipulate logical inputs and produce a single output based on their truth values.

3. How do you solve a Boolean logic expression using AND, OR, and NOT gates?

To solve a Boolean logic expression, you must first break it down into smaller sub-expressions and then use the AND, OR, and NOT gates to evaluate the truth values of each sub-expression. These truth values can then be combined to determine the overall truth value of the original expression.

4. What are truth tables and how are they used in solving Boolean logic expressions?

A truth table is a table that shows all possible combinations of inputs and their corresponding outputs for a given Boolean logic expression. Truth tables are useful in solving Boolean logic expressions because they provide a systematic way to evaluate the truth values of each sub-expression and determine the overall truth value of the original expression.

5. Can Boolean logic be applied to real-world problems?

Yes, Boolean logic can be applied to real-world problems. It is commonly used in computer programming to make decisions based on user input or system conditions. It is also used in electrical engineering to design and analyze digital circuits.

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