We discussed how we could modify the $4$bit ALU to support detecting overflow but did not give the proof. Now you are expected to prove you can detect overflow by simply check if Carry into MSB $!=$ Carry out of MSB$.$

Hint: you could use a table $($like a truth table$)$ to list all situations, then identify the cases that cause overflows

$\backslash$table$[[\backslash$table$[[$Sign bit of$],[$operand A$]],\backslash$table$[[$Sign bit of$],[$operand B$]],\backslash$table$[[$Carry into$],[$MSB$]],\backslash$table$[[$Sign bit$],[$of result$]],\backslash$table$[[$Carry out$],[$of MSB$]],$Overflow?,Comments$],[0,0,0,,,,],[0,0,1,,,,],[0,1,0,,,,],[0,1,1,,,,],[1,0,0,,,,],[1,0,1,,,,],[1,1,0,,,,],[1,1,1,,,,]]$