How do you design a combinational circuit with three inputs and three outputs?

For my computer organization class homework, one question reads “Design a combinational circuit with three inputs x, y, z and three outputs A, B, C. When the input is 0, 1, 2, or 3, the binary output is one greater than the input. When the binary input is 4, 5, 6, or 7, the binary output is one less than input.”
I’m not looking for the answer, just a little guidance, I just need to be pointed in the right direction. I really have no clue what to do. Thanks a lot!

One approach would be to write out the truth tables for each output, then determine what combination of logic functions will generate such truth tables:

I2 I1 I0 – O2 O1 O0
0 0 0 – 0 0 1
0 0 1 – 0 1 0
0 1 0 – 0 1 1
0 1 1 – 1 0 0
1 0 0 – 0 1 1
1 0 1 – 1 0 0
1 1 0 – 1 0 1
1 1 1 – 1 1 0

O0 (lsb) is clearly just the complement of I0.

O1 is achieved via the exclusive-or of all three inputs (i.e. parity).

O2 is true when (and only when) at least two inputs are true. This could be accomplished by ANDing each pair of inputs, then ORing those three results. There are many other ways of course, this is just one of the obvious ones.

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