Design a Mealy sequential circuit to convert a $4-$bit binary number in the

range $0000$ through $1010$ to its $10\text{'}$s complement. $($The $10\text{'}$s complement of

a number $N$ is defined as $10-N.)$ The input and output should be serial with

the least significant bit first. The input $x$ represents the $4-$bit binary number,

and the output $z$ represents the corresponding $10\text{'}$s complement. After four

time steps, the circuit should be reset to the starting state regardless of the

input sequence.

Find a state table with a minimum number of states. Design the circuit using

three JK flip$-$flops and external gates as required. Assign $000$ to the reset

state.