A sequence recognizer $M$ has an input $x$ and outputs $(Y$ and $Z).YZ$ represents a $2-$bit

binary number equal to the number of pairs of adjacent $1\text{'}$s that have been received as

inputs where $Y$ is the MSB$.$ For example, the input sequence $0110$ contains one pair,

the sequence $01110$ two pairs, and the sequence $0110111$ contains three pairs of

adjacent $1\text{'}$s$.$ The circuit resets when the total number of pairs of $1\text{'}$s received reaches

four.

Examples:

a$)$ Draw a Moore state diagram for the sequence recognizer $M.$

b$)$ Determine the state table for M with D Flip$-$flops' excitation.

c$)$ Determine the output functions of $M$ to minimum SOP forms.

d$)$ Minimize the D flip$-$flops' input functions to minimum SOP forms