Converting logic circuit to using only 2-input NAND gates and NOT gate

In summary, the conversation discusses converting a logic circuit to an equivalent circuit using 2-input NAND and NOT gates. The person is struggling with converting a 3-input OR gate to a 2-input NAND gate and asks for help. They are advised to use Boolean algebra to simplify the equation and convert all OR operations to AND/NAND.
  • #1
colerelm
2
0

Homework Statement


Convert the logic circuit to an equivalent circuit constructed from 2-input NAND gates and NOT gates.
http://imgur.com/EzOBdbv

Homework Equations


Pretty sure the boolean equation is:
A & (~(~B+C)+~D + E)

The Attempt at a Solution


I know for sure that ~A + ~B = ~AB so I was trying to add an inverter to the input of each OR gate to try to make use of this equation but I get stuck at the spot where I need to convert a 3-input OR gate to a two input NAND gate. Can anyone please help?
 
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  • #2


Hi colerelm, http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif
A & (~(~B+C)+~D + E)
You need to convert all the OR operations to AND/NAND. It is usually best to do this as Boolean algebra, rather than piece by piece in the logic gates diagram. The latter may not be simplest, and it's difficult to spot redundancy. (EDIT: why not try it both ways, and see whether they give the same result here?)

Q: How to fabricate a 3-input NAND gate using 2-input NAND gates? Can you do that?
 
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1. How can I convert a logic circuit to only use 2-input NAND gates and a NOT gate?

To convert a logic circuit to use only 2-input NAND gates and a NOT gate, you will need to first identify the logic gates present in the original circuit. Then, use De Morgan's Laws to convert each gate into an equivalent combination of NAND gates and NOT gates. Finally, simplify the resulting circuit by identifying common inputs and outputs to reduce the number of gates needed.

2. Why would I want to convert a logic circuit to only use 2-input NAND gates and a NOT gate?

Converting a logic circuit to use only 2-input NAND gates and a NOT gate can have several benefits. It can reduce the number of unique gate types needed, simplifying the design and potentially reducing costs. It can also make the circuit more versatile, as NAND gates are universal gates and can be used to implement any other gate type.

3. Is it possible to convert any logic circuit to only use 2-input NAND gates and a NOT gate?

Yes, it is possible to convert any logic circuit to only use 2-input NAND gates and a NOT gate. This is because NAND gates are universal gates, meaning they can be used to implement any other gate type. Therefore, any logic circuit can be converted to use only NAND gates and a NOT gate.

4. Are there any limitations to converting a logic circuit to only use 2-input NAND gates and a NOT gate?

While it is possible to convert any logic circuit to only use 2-input NAND gates and a NOT gate, there may be limitations in terms of the complexity and size of the resulting circuit. In some cases, the converted circuit may be larger and more complex than the original circuit. Additionally, converting a circuit to only use NAND gates and a NOT gate may not always be the most efficient or practical solution.

5. Can I use other combinations of gates besides 2-input NAND gates and a NOT gate?

Yes, there are other combinations of gates that can be used to implement any logic circuit. Some commonly used combinations include NOR gates and a NOT gate, as well as AND and OR gates with NOT gates. However, using 2-input NAND gates and a NOT gate is a popular choice due to the simplicity and versatility of NAND gates.

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