$1.$ Design a circuit with four inputs i$,$ j$,$ x$,$ y$,$ and two outputs b$,$ c$.$ Each of these values is one bit. Use $4-$variable Karnaugh maps with don$$t cares to minimize the functions for outputs b and c$.$

The circuit will implement all three functions below. Inputs i and j are control inputs that will select one function, then inputs x and y are data inputs that will determine outputs b and c according to the selected function. Assign $($and specify in your design$)$ control input values to the functions. For instance, if you assign ij $=00$ to Function F$,$ then the inputs i $=0,$ j $=0,$ x $=0,$ y $=1$ will generate the outputs b $=1,$ c $=0.$

For a function with only one specified output, the values for the other output are don$$t cares. $($For example, for Function G$,$ the c outputs are don$$t cares.$)$

Function F

r s b c

$0000$

$0110$

$1011$

$11$ d d

Function G

r s b

$000$

$011$

$101$

$111$

Function H

r s c

$000$

$011$

$100$

$110$

The better your minimization, the easier wiring up a circuit would be$.$

$2.$ Draw your circuit of logic gates.

$3.$ Draw truth tables for b and c as you have implemented them after simplification. Note that these truth tables will not have don$$t care entries because your implementation will produce an output value for each combination of inputs

$4.$ Did you combine terms between outputs b and c$?$ If so$,$ then explain details. If not, then could you have done so$?$