Logic Gate question

[Bluga]

Link page6

On page6 of the PDF, why is f = x1+x2 ? I used Karnough map but that didn't get the answer.

Thanks the help.

 

[SinNisTeR]

here is a bump for ya.. man this stuff looks like alien sh!t.

 

[Sahakiel]

3 input binary. m(1,2,3) = 001, 010, 011.
[edit]minumum sum of products form: f= /x2 /x1 x3 + /x2 x1 /x0 + /x2 x1 x0[/edit]

 

[Bluga]

<< 3 input binary. m(1,2,3) = 001, 010, 011. >>



K-map gets me f = (x1)' ( x2 + x3) but can it be simplified more?

 

[Sahakiel]

I think your prof screwed up. The first line in the 3-input solution is the solution for 2-input. Stop focusing on it.
Your k-map is correct, but is written using ANDs and ORs. Use, um, I think it was Lagrange? not sure. Basically, rewrite it using NANDs and NORs and you should get the second line in the solution.
f=(x1)' (x2 + x3)
substitute NOR for the AND and you get
f=( (x1) + (x2 + x3)' )' the beginning of the second line in the 3-input solution. Don't believe me, make a truth table. x'y=(x + y')'
Personally, I'd have gone the 2-input way. A single NOR and an inverter is what first popped into my head. In case you're wondering, a single input into both NAND inputs equals a NOT.

 

[Alphathree33]

Well I looked at the first question for about ten minutes to see if I could find out how to do that question in general.

And I still have no clue what's going on nor could I find a pattern relating x1, x2 and x3 to the diagram 🙁 hehe.

But I will be in first year engineering next year. Maybe then I can help. 🙂

As for your question about page 6, I have about as much of a clue as I did on the first question.