Designing Logic Gates for Multiple Inputs and Outputs in Homework Problems

[seto6]

Homework Statement

ok there are two questions. one i was able to do so which is fairly easy, since it had only two variables and one output.

Design a circuit that has two inputs (x and y) and one output (f) that functions in the
following way: the function f is false (0) when x and y are the same, and true (1)
when they are different.

my answer:

and its fine now comes this question:

Design a circuit with three inputs (a,b, and c) and three outputs (f1, f2, and f3). The
first output (f1) should be true (1) whenever the number of 1’s in the three inputs is 2.
The second output (f2) should be true (1) whenever the number of 0’s in the three
inputs is 1. The third output (f3) should be true (1) whenever the number of 0’s in the
three inputs is 3. In all other cases, the outputs should be false (0).
Optional: using all of the gates available, can you build a cheaper implementation
(using fewer gates and/or wires)?

Homework Equations

N/A

The Attempt at a Solution

for the second question this is what i did:

as you can see i am now stuck for drawing the logic gate, and stating what the function is equal.

even if three var i am ok, but it is three output.

Important question: for which do i draw logic gates for as you know for the first question i drew when f=1, so for second question, which do i draw gates for, (should i draw for any that has a one in it?)


Thank you in advance

 

[JeSuisConf]

It's not clear what you're asking. But clearly $$f_1 = f_2$$, and it is given by

$$f_1=f_2=\bar{a}bc + a(b\bar{c}+\bar{b}c)$$

and $$f_3$$ is given by

$$f_3=\bar{a}\bar{b}\bar{c}$$.

Also, it is generally bad form to not order your inputs by standard binary ordering.