This assignment asks you to express a particular logical idea using a limited and unintuitive set of logical operators.

The work is very detailed, and you may experience a struggle to maintain and confirm logical equivalence. That

struggle is part of the point. At some point in your future career, you will likely be tasked with "system migration,"

either directly translating one system's task for another system to execute, or by designing a tool to do so$.$ You

might consider this assignment as a preview of the challenges of system migration.

Context

p q r s output

T T T T F

T T T F F

T T F T F

T T F F F

T F T T F

T F T F T

T F F T T

T F F F F

F T T T F

F T T F T

F T F T T

F T F F F

F F T T F

F F T F F

F F F T F

F F F F F

Imagine an electronic switch with four input wires arranged in two

pairs, as illustrated in the diagram at the right. To allow current to

flow, the switch must be activated by a voltage from exactly one

input wire in each pair. A second wire from either pair acts as an

inhibitor and stops the current flow.

Let p$,$ q$,$ r$,$ and s represent the input voltages of the four wires,

respectvely, with p and q making up the first pair and r and s

making up the second pair. A "true" value indicates a voltage in

that wire. Then the logic of the switch is represented in the truth

table at left.

As we saw in class, the NAND operator by itself forms a fundamental set of logical

operators. That is$,$ every logical relationship can be expressed in terms of NAND.

Now imagine a hardware protocol with negations $($~$)$ and conditionals $()$ as its

fundamental operators, and imagine constructing this switch under that protocol.