Part $3.$ Half Subtractor

The half subtractor and full subtractor work much the same way as their adder counterparts except we are subtracting the numbers instead of adding them. In the half subtractor we have two single place inputs, $S1$ and $S2$ that are subtracted from each other $($S$1-$S$2).$ The outputs $($LED$1$ & $2)$ show the result $($difference$)$ and whether or not a 'borrow' occurred $($borrow$).$

a$)$ Design a Half Subtractor using a truth table and a Karnaugh map. Construct the Half Subtractor using Logisim.

b$)$ Simulate the Half Subtractor: vary the inputs and construct a truth table showing your results.

c$)$ What effect does a negative result have on the outputs? $)=(-1$