A sequential circuit has one input $x$ and two outputs $Z_1$ and $Z_2.$ An output $Z_1=1$

occurs every time the input sequence $000$ is complete provided that the sequence $111$

has never occurred. An output $Z_2=1$ occurs every time the input $111$ is complete,

provided the sequence $000$ has never occurred. Note that once a $Z_1=1$ output has

occurred, $Z_2=1$ can never occur, and vice$-$versa.

Draw a Mealy state diagram.

Assign binary labels to the states according to a "one$-$hot" encoding, and write

Boolean expressions for the next states and the outputs.