Need a help in making logic circuits

[Ph_Student]

Homework Statement

So I have four bits input(X0,X1,X2,X3), and I need to check if these four bits are monotonic sequence. I got the following function:


Y0 = X2X1X0 + X3'X2'X1' + X3'X2'X0
(Y0 - the output 1 when X0>=X1>=X2>=X3)

Y1 = X2'X1'X0' + X3X1'X0' + X3X2X1'
(Y1 - The output 1 when X0<=X1<=X2<=X3)

I need to make a logic circuit with the minimum number of logic Gate, I also can use only two input gate.

Homework Equations

The Attempt at a Solution

I got 14 gates, I tried to use NAND and XOR gates, but it didn't work for me. Can anyone make any suggestion on how can I make it with less gates.

Thanks

 

[cybernoodles]

Try putting the logic equation you've come up with into a Karnaugh map to reduce it or you can just perform some boolean algebra to simplify the original equation using properties such as demorgans theorem etc.

 

[LCKurtz]

But don't you want a single output function Y and a boolean formula for it in terms of the inputs? Calling the inputs a,b,c,d instead of X0 etc, I get

Y = abd' + a'b'd + bcd + b'c'd'

5 gates if you are allowed 4 input OR and 3 input AND with inverted inputs, but hey, that part is your problem.

 

[Ph_Student]

I already handed the homework, but thanks guys

LCKurtz: I wanted two outputs, one if its increasing monotonic, and one if its decreasing monotonic sequence. And I also can use only two input gates.
and the efficiency was to find less gates using nand or nor, because the given deletion time for these gate is low.

but thanks anyway I got 97/100 :-)

 

[vela]

How many gates did you get it down to?

 

[Ph_Student]

12 NOR gates