December $11,2024$

Instructions: You have $24$ hours to complete this test. I am more interested in seeing you work toward a correct solution than the correct solution itself, so please show your work. Please upload the solutions by $12$:$30$ PM on December $12$th$.$ Late submissions will not be graded.

Scenario: You have been hired on a coffee farm to design a harvesting robot.

The operation of the robot is shown in Figure $1.$ The robot needs to move between rows of coffee trees in a back and forth manner, picking cherries as it goes. The operation is as follows:

$1)$ The robot will start at the lower right hand side of the plot. It will move along the length of a row with the trees on its left until it detects the edge of that row $($i$.$e$.$ no trees$)$

$2)$ Then, it will turn to the left and move the width of the tree row $($with trees on its left$)$ until it detects no trees.

$3)$ At this point, the robot will move to harvest a new row of trees. It will move along the length of this new row with the trees on its right until it

detects no more trees.

$4)$ Then, it will turn to the right and move the width of the tree row $($with trees on its right$)$ until it detects no trees.

$5)$At this point, the robot will move to harvest a new row of trees. It will move along the length of this new row with the trees on its left until it detects no more trees.

The above steps must continue until the robot finds the end of the plot. The size $($i$.$e$.$ number of rows$)$ of the plot should not matter.

$6)$ The end of the plot will occur when the robot makes a turn but detects no trees.

$7)$ This will cause the robot to enter an idle state in which it will remain until the system has a hard reset.

Problem $1$a: Draw a finite state diagram for the harvester robot. Is it a Mealy or Moore machine? $(3$ points$)$

Problem $1$b: Provide the truth tables for both the output logic and state evolution logic $(1$ point$).$

Problem $1$c: Provide full POS equations for both output and evolution logic $(1$ point$).$

Problem $1$d Using Karnaugh maps, derive the simplest boolean algebra equations for the output logic and state evolution logic $(2$ points$).$

Problem $1$e Draw the full circuit that would implement this device using only universal gates $(2$ points$).$

Problem if Draw the full circuit that would implement this device using only decoders $(2$ points$).$