$1.$ LC$-3$ condition codes

The LC$-3$ has three condition code flip$-$flops N$,$ Z$,$ and P$.$ The states of these flip$-$flops indicate whether the last value on the processor bus was a negative, zero, or positive number in two's$-$complement representation. The P flip$-$flop is not necessary.

Redefine the BR instruction format so that bit IR$[9]=1$ means "NOT", and IR$[11]$ and IR$[10]$ retain their meanings, checking flip$-$flops N and Z$.$ Write a table with eight entries for IR$[11$:$9]=000,...,111$ and explain what kind of branch condition each defines. For example, with the new format, IR$[11$:$9]=111$ means branch if not $($negative or zero$),$ that is$,$ branch if positive.

Redefine the boolean expression for the BEN flip$-$flop in State $32$ of the LC$-3$ state machine for this new BR instruction format. Hint: have we seen a method to control whether a Boolean expression is inverted or not?