Logic Gates (NAND to AND Gates)

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Discussion Overview

The discussion revolves around the logic behind the transformation of NAND gate inputs to construct an AND gate. Participants explore the representation of inputs and outputs in terms of logical expressions, specifically focusing on the expression ( (XY)' (XY)' ) ' and its simplification.

Discussion Character

  • Technical explanation, Debate/contested

Main Points Raised

  • One participant expresses confusion about the expression ( (XY)' (XY)' ) ', suggesting it should be ((XY)' ) ' since the second gate acts as an inverter for the first gate's output.
  • Another participant explains that the expression (XY)'(XY)' is correct because both inputs to the second gate are tied together, leading to the output being ( (XY)' (XY)' ) ', which can be simplified to ( (XY)' ) ' and ultimately to XY, demonstrating how two NAND gates can create an AND gate.
  • A later reply reiterates the previous explanation and questions whether the input can be represented as ((XY)' ) ', which can also be simplified to XY.
  • One participant agrees with the simplification proposed in the previous posts.

Areas of Agreement / Disagreement

Participants express differing views on the correct representation of the input to the second gate, with some supporting the original expression and others advocating for the alternative representation. The discussion remains unresolved regarding the preferred notation.

Contextual Notes

There are assumptions regarding the understanding of logic gate operations and the simplification of logical expressions that are not explicitly stated. The discussion relies on the definitions of NAND and AND gates and their interrelations.

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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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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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 ?
 
Yes, I believe that's right.
 
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