Pretty simple NAND gate question

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The discussion centers on the equivalence of two expressions involving NAND gates: x1↑(x2↑x2) and x2↑(x1↑x2). Participants analyze the truth tables for these expressions and a related XOR expression, x1¬x2 + x2¬x1, which is confirmed to be equivalent to XOR. There is confusion regarding the interpretation of the NAND operator (↑) and its implications for the circuit design. Ultimately, it is clarified that the two original expressions are not identical, as they yield different outputs based on the truth tables. The conversation highlights the importance of clear definitions in digital logic to avoid misunderstandings.
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Homework Statement



I was looking through some examples in my Digital Logic book and I stumbled across one that gave an answer of x1\uparrow(x2\uparrowx2). The answer I got was x2\uparrow(x1\uparrowx2).

After making a truth table I'm finding that these are not equal solutions. Unless, I'm doing something wrong.

The Attempt at a Solution



See above. Any help is appreciated.
 
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DrummingAtom said:
x1\uparrow(x2\uparrowx2).
Can you write this in words so I can see where NAND comes into it?
 
NascentOxygen said:
Can you write this in words so I can see where NAND comes into it?

The problem asked to turn x1\overline{x}2 + x2\overline{x}1 into a NAND only circuit. I used decomposition in the last steps to get my answer.
 
DrummingAtom said:
The problem asked to turn x1\overline{x}2 + x2\overline{x}1 into a NAND only circuit. I used decomposition in the last steps to get my answer.
Can you show the truth table for x1\overline{x}2 + x2\overline{x}1? I'm not sure the book answer is correct assuming that ↑ means NAND.
 
I got my question answered today in class. Those two solutions are equivalent. Thanks for the help though.
 
I'm somewhat confused by this. You never explained what ↑ means.

Isn't x1\overline{x}2 + x2\overline{x}1 the same as XOR? Wiki article for XOR implemented with NAND gates:

http://en.wikipedia.org/wiki/NAND_logic#XOR
 
According to my book, ↑, is a NAND gate operator.
 
OK, so again I ask what is the truth table for

x1\overline{x}2 + x2\overline{x}1

and the truth table for

x1↑(x2↑x2)

or

x2↑(x1↑x2)
 
DrummingAtom said:
According to my book, ↑, is a NAND gate operator.
But a poor choice, and bound to lead to confusion.
 
  • #10
rcgldr said:
OK, so again I ask what is the truth table for

x1\overline{x}2 + x2\overline{x}1
Yes, that is exclusive NOR.

and the truth table for

x1↑(x2↑x2)

or

x2↑(x1↑x2)

x2 NAND x2 is just NOT x2

x2↑(x1↑x2) evaluates to x2 NAND NOT x1

So expressions in post #1 are NOT identical.
 
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