Logic Circuit Conversion Homework: NAND-NOR to AND-OR and Back to NAND-NOR

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In summary, The conversation is about converting a NAND-NOR circuit to a simpler AND-OR circuit with an AND gate output, and then converting it back to a NAND-NOR circuit with a NOR gate output. The solution involves drawing the circuit in two parts, with part a) resulting in a simplest AND-OR circuit and part b) resulting in a NOR output. There is also a clarification about swapping NOT gates in the last diagram.
  • #1
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Homework Statement



1. Convert the following NAND-NOR circuit to simplest AND-OR circuit (bubbles allowed) such that the output gate is an AND. Then, convert the resulting circuit back into a NAND-NOR circuit (no bubbles) such that the output gate is a NOR.

Screen Shot 2015-02-15 at 11.44.50 AM.png


Homework Equations

The Attempt at a Solution



My solution is drawn in two parts, part a) and b).

For part a) I believe I got the simplest AND-OR circuit possible with an AND gate output.

For part b) I am unsure if the circuit is as simple as possible, but I managed to get a NOR output.

My work is shown below:

IMG_0526.jpg


Do these look okay?

Thank you.
 
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  • #2
Zondrina said:
Do these look okay?
Seems OK.
 
  • #3
Looks right.
For clarification, I would swap the two NOT for A and B in the last diagram (so the upper gate keeps the same meaning as before), but that does not change how the circuit works.
 
  • #4
For that matter, the upper left combination is an XOR:
upload_2015-2-15_18-41-9.png
 

1. What is logic circuit conversion?

Logic circuit conversion is the process of converting one type of logic circuit to another, typically using Boolean algebra and logic gates. This is often done to simplify a circuit, reduce costs, or improve performance.

2. What are the different types of logic circuit conversion?

There are three main types of logic circuit conversion: NAND-to-AND, NOR-to-OR, and De Morgan's theorem conversion. NAND-to-AND conversion involves replacing all NAND gates with AND gates and inverting the output. NOR-to-OR conversion is similar, replacing NOR gates with OR gates and inverting the output. De Morgan's theorem conversion involves applying De Morgan's theorem to a circuit to simplify it.

3. What are the benefits of logic circuit conversion?

Logic circuit conversion can provide several benefits, including reducing the number of gates in a circuit, increasing the speed of the circuit, and reducing the cost of the circuit. It can also make the circuit easier to understand and troubleshoot.

4. How do you convert a logic circuit?

To convert a logic circuit, you first need to analyze the circuit and identify its components, such as logic gates and inputs. Next, you can use Boolean algebra and logic gates to manipulate the circuit and simplify it. You may also need to use De Morgan's theorem or other conversion techniques depending on the type of conversion needed.

5. What are some common applications of logic circuit conversion?

Logic circuit conversion is commonly used in digital electronics, such as in computer processors, to optimize and simplify circuits for better performance. It is also used in telecommunications, control systems, and other electronic applications to improve efficiency and reduce costs.

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