Please design a $2-$ stage logic micro$-$operations circuit using J$-$K flip$-$flops using the imaged logic operations. Include a drawing of the circuit, including all work done to derive the circuit, including any relevant tables and k $-$ maps.

The first micro$-$operation, Ai Ai V Bi$\text{'}$ is a nameless micro$-$operation the boolean function F$11=$x$+$y$\text{'}$

The second micro$-$operation, Ai Ai$\text{'}\backslash$Lambda Bi is a nameless micro$-$operation, with the boolean function F$4=$x$\text{'}$y

The third micro$-$operation, Ai Ai V Bi$)\text{'}$ is the NOR micro$-$operation, with the boolean fuction F$8=($x$+$y$)\text{'}$

The fourth micro$-$operation, Ai Ai $\backslash$Lambda Bi$)\text{'}$ the NAND micro$-$operation, with the boolean function F$14=($xy$)\text{'}$

The fifth micro$-$operation, Ai Ai $$ Bi is the XOR micro$-$operation, with the boolean function F$6=$ X $$ Y

The fifth micro$-$operation, XOR, can be implemented$/$wired by connecting input pins Bi and another input pin into the inputs of an AND, and connecting the output of the AND into both J and K inputs of a JK flip$-$flop, connecting the output Q into output bit Ai$.$ A clock pin goes into the clock input of the JK flip$-$flop. I am not sure how the other micro$-$operations are wired.

The flip$-$flop state table for XOR is as follows

$|$PS $|$ INPUT $|$ NEXT STATE $|$ FF INPUTS$|$

$|$Ai $|$ Bi $|$ Ai $|$ JAi KAi $|$

$----------------------$

$|0|0|0|0$ x $|$

$|0|1|1|1$ x $|$

$|1|0|1|$ x $0|$

$|1|1|0|$ x $1|$

The appropiate k$-$maps for XOR would be as follows

Ai$\backslash$Bi$|0|1|$

$0|0|1|$

$1|$x$\}$x$|$

JAi$=$Bi

Ai$\backslash$Bi$|0|1|$

$0|$x$|$x$|$

$1|1|1|$

KAi$=$Bi

Such tables and k$-$maps for all micro$-$operations are required. Please refer to a truth table and excitation table of the JK flip$-$flop if needed.

For the two$-$stage circuit, create one circuit with input B$0$ and output A$0,$ and another circuit with input B$1$ and output A$1.$ Both will have a common set of T inputs. I believe the circuit might use a single JK flip$-$flop, but I am not certain.