Design a one$-$input and one$-$output synchronous binary Moore Machine that detects the occurrence of two specific $3-$bit binary sequences $010$ and $001($left hand start for both sequences$)$ defined as below:

$1)$ If no specific sequence is detected, the output is to be $00.$

$2)$ If $010$ is detected, the output $01$ is generated.

$3)$ If $001$ is detected, the output $11$ is generated.

$4)$ Do not distinguish which sequence is coming first.

$5)$ Two sequences must be detected by using ONE circuit block. Using two separate circuits to detect the sequences individually will NOT receive marks.

$6)$ Overlapping sequences should be detected.

$7)$ You can choose to use either JK or T flip$-$flops, but a minimum number of flipflops and external gates must be used in the selected design.

Give detailed design procedures including state diagram, state tables, binary representation, logic simplification procedures and logic circuit diagrams, etc.