Design a Moore pattern detector that outputs z$=1$ if the $3-$bit input sequence x$=101$ is detected and

outputs z$=0$ otherwise. Allow for overlaps. For example:

x$=001101110101000$dots

y$=000000100010100$

Your answer must include a state diagram, state table, state assignment, state transition and output

tables, minimization K$-$maps, and excitation and output equations. Verify if the number of states can

be reduced or not. Use D$-$FFs$.$