Pretty simple NAND gate question

[DrummingAtom]

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$\uparrow$x₂). The answer I got was x₂$\uparrow$(x₁$\uparrow$x₂).

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.

 

[NascentOxygen]

x₁$\uparrow$(x₂$\uparrow$x₂).

Can you write this in words so I can see where NAND comes into it?

 

[DrummingAtom]

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.

 

[rcgldr]

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.

 

[DrummingAtom]

I got my question answered today in class. Those two solutions are equivalent. Thanks for the help though.

 

[rcgldr]

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

 

[DrummingAtom]

According to my book, ↑, is a NAND gate operator.

 

[rcgldr]

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)

 

[NascentOxygen]

According to my book, ↑, is a NAND gate operator.

But a poor choice, and bound to lead to confusion.

 

[NascentOxygen]

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.