Converting logic diagram to only NAND gates

In summary, a NAND gate can be used as an inverter by connecting both inputs together and the output will be the inverse of the input. Alternatively, one input can be connected to a logic 1 to achieve the same result.
  • #1
LongApple
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Homework Statement



How is he able to just swap the inverter for a NAND gate? Doesn't a NAND gate require two things?

See the text on the right for his explanation
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Homework Equations

The Attempt at a Solution

 
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  • #2
LongApple said:
How is he able to just swap the inverter for a NAND gate? Doesn't a NAND gate require two things?
What sort of "things" did you have in mind? If the inputs are tied together then the only inputs available to the NAND are both inputs "1" or both inputs "0". What does a NAND gate output for each case?
 
  • #3
LongApple said:
How is he able to just swap the inverter for a NAND gate?
So, we are revisiting this topic! :) We thought you would learn about the NAND inverter from your previous thread, but I think you dropped out and didn't see it through to its conclusion.

You can join the two inputs together, which gives both inputs either 1 or both inputs 0, and the output becomes the NOT of this. So, yes, a NAND gate with a signal applied to both its inputs acts as a NOT gate.
 
  • #4
Or look at it this way.. The NAND truth table is

00=1
01=1
10=1
11=0

if both inputs are wired together they are always the same, so the only combinations that can occur are..

00=1
11=0

There is another way to turn a NAND gate into an inverter - You could just connect one input to a logic 1 permanently...

10=1
11=0
 

Related to Converting logic diagram to only NAND gates

1. How do you convert a logic diagram to only NAND gates?

To convert a logic diagram to only NAND gates, you need to first identify all the gates and their corresponding truth tables in the original diagram. Then, you can use De Morgan's laws to express each gate as a combination of NAND gates. Finally, you can simplify the resulting expression to use only NAND gates.

2. What is De Morgan's law and how is it used in converting to NAND gates?

De Morgan's laws state that the complement of a logical expression can be expressed by interchanging the logical operators AND and OR, and complementing each term. In converting to NAND gates, these laws are used to express AND and OR gates as combinations of NAND gates.

3. Can any logic diagram be converted to only NAND gates?

Yes, any logic diagram can be converted to only NAND gates using De Morgan's laws and simplification techniques. However, the resulting circuit may not be the most efficient in terms of speed or cost.

4. Are there any advantages to using only NAND gates in a circuit?

One advantage of using only NAND gates in a circuit is that they are versatile and can be used to implement any logical function. Additionally, using only one type of gate can simplify the design and reduce the number of components needed.

5. Are there any limitations to using only NAND gates in a circuit?

One limitation of using only NAND gates is that the resulting circuit may not be the most efficient in terms of speed or cost. Additionally, some logical expressions may require more NAND gates compared to other types of gates, which can lead to a more complex circuit.

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