logic gates question

[EngIntoHW]

Hey,
Could you please help me with the following question?

Given Two 4 bit nos
A= 1001
B = 1100
HOW DO YOU XOR them using minimum number of gates? How do you nand them? How do your or them? (Hint: 4:1 Muxes)

It's possible to compute A XOR B using 4 units of 4:1 Mux (same goes to A NAND B, A OR B), but I dont see how its minumum.

Thanks.

 

[MrAl]

Hi,

Can you use four XOR gates, or do you have to restrict to nand, and, or, nor, not?

 

[EngIntoHW]

I guess that in order to compute A XOR B, I'm not allowed to use XOR gates.

It's weird: Ai XOR Bi = Ai(Bi') + (Ai')Bi => 3 gates.
However, 4:1 Mux requires more gates.

 

[MrAl]

Hi again,


I guess you also have to specify the problem a little more clearly too. For example, can you use four input gates or just two input gates, and does a NOT (inverter) count as one gate or can you negate an input or output any time you feel like it and not cause an addition of one more gate?
Also, when you say, "Mux", do you mean a four to one multiplexer, and does that add as one gate or do you have to construct the multiplexer with gates too?

The other mapping for the XOR is:
C=(A+B)*(A'+B')

if that helps any.

 

[EngIntoHW]

Got you MrAl,

Thanks.

The question is indeed not clear enough.

You gave me good points of thinking.