Design a combinational circuit with three inputs: $x,y,z$ and three outputs: $A,B,C,$ such that,

When the binary input $xyz$ represents the decimal digits: $0,1,2,3,$ or $6,$ the binary output ABC

should correspondingly represent the decimal digits $1,2,6,4,$ and $5.$

The remaining three, binary input representations of the decimal digits $4,5,$ and $7$ do not occur.

a$)$ First, make the truth table with $3$ input columns and $3$ output columns for the functions $A,B,$ and $C.$

b$)$ Next, usind'three separate K$-$Maps find the minimal forms of these $3$ functions.

c$)$ Finally, draw a circuit with $3$ inputs and $3$ outputs, representing one minimal form of these $3$ functions.