Logic Gates (NAND to AND Gates)

In summary: The reason for this is because the second logic gates receive (XY)' as input from the first logic gates, and they act as an inverter for the (XY)' input. This allows the output to be simplified to ( (XY)' ) ' and then further reduced to simply XY, demonstrating that two NAND gates can be used to construct an AND gate.
  • #1
desmond iking
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couldnt understand why the input is ( (XY)' (XY)' ) ' , IMO , it should be ((XY)' ) ' . because the 2nd logic gates receive (XY)' input from the first logic gates , and the second logic gates act as inverter for the first logic gates.
 

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  • #2
I think they did that because the (XY)' is the input to the second gate and both inputs are tied together then they said (XY)'(XY)' and the second gates output is then ( (XY)' (XY)' ) ' which can be reduced to ( (XY)' ) ' and the double negative to simply XY so it shows that two NAND gates can be used to construct an AND gate.
 
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  • #3
jedishrfu said:
I think they did that because the (XY)' is the input to the second gate and both inputs are tied together then they said (XY)'(XY)' and the second gates output is then ( (XY)' (XY)' ) ' which can be reduced to ( (XY)' ) ' and the double negative to simply XY so it shows that two NAND gates can be used to construct an AND gate.
Can I say the input is ((XY)' ) ' , which is also can be reduced to XY ?
 
  • #5


There are a few things to consider when discussing the input for NAND to AND gates. First, it's important to remember that NAND gates are essentially inverted AND gates. This means that the output of a NAND gate will be the opposite of what an AND gate would produce.

In this case, the input is ( (XY)' (XY)' ) ', which may seem confusing at first. However, when we break it down, we can see that the first (XY)' represents the output of the first NAND gate, which is then being inverted by the second NAND gate. The second (XY)' represents the output of the second NAND gate, which is then being inverted by the final NOT gate.

Essentially, the (XY)' input is being inverted twice, first by the second NAND gate and then by the final NOT gate, to produce the final output of the AND gate. This is necessary because, as mentioned earlier, NAND gates are inverted AND gates, so we need to invert the input twice to get the desired output.

In summary, the input for NAND to AND gates may seem unintuitive at first, but it is necessary in order to get the desired output. It is important to understand the properties of NAND gates and how they differ from AND gates in order to properly design and use logic gates in scientific research.
 

1. What are logic gates and how do they work?

Logic gates are electronic circuits that perform logical operations on one or more binary inputs to produce a single binary output. They work by using transistors to control the flow of electricity and create different logical states (0 or 1) based on the input values.

2. What is the difference between a NAND gate and an AND gate?

A NAND gate is a combination of an AND gate and a NOT gate. It produces a 0 output only when both inputs are 1, and produces a 1 output for all other combinations. An AND gate produces a 1 output only when both inputs are 1, and produces a 0 output for all other combinations.

3. How are NAND gates and AND gates used in digital circuits?

NAND and AND gates are commonly used as building blocks for more complex logical operations in digital circuits. They can be connected together in various combinations to perform tasks such as data processing, signal routing, and error detection in computers and other electronic devices.

4. Can NAND gates and AND gates be used for other purposes besides logic operations?

Yes, NAND and AND gates can also be used as amplifiers and inverters in electronic circuits. They can also be used in voltage level conversion and signal restoration in digital systems.

5. How do you troubleshoot issues with NAND and AND gates in a circuit?

To troubleshoot issues with NAND and AND gates, you can use a multimeter to check for proper voltage levels and continuity. You can also use a logic probe to determine if the gates are functioning correctly. If there are still issues, you may need to replace the gates or check for any loose connections in the circuit.

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