Answer the following with proper reasoning and explainations:The ALU within the single$-$cycle datapath outputs a $32-$bit data result $($R$31,$

R$30,...,$ R$1,$ RO$)$ along with a single$-$bit zero flag $($ZERO$).$ Write down a logic

expression that gives ZERO as a logic function of the $32-$bit result.

ZERO $=$

The MIPS addu instruction performs the same operation as the MIPS add

instruction. The only difference is that add triggers an exception if the

addition results in a signed overflow, while addu does not. The instruction

addu $$4,$$$5,$ $$6$ places into register $$4$ the $32-$bit sum of the contents of

register $$6$ plus the contents of register $$5.$ Answer the following questions

about the instruction addu $$4,$$$5,$$$6$ :

a$)(3)$ If registers $$5$ and $$6$ contain integers that differ in sign, can the result

in $$4$ be incorrect due to an overflow? Explain your answer.

b$)(3)$ If an overflow does not occur and registers $$5$ and $$6$ both contain a

negative integer, what will be the sign of the result in $$4?$

c$)(3)$ If an overflow does occur and registers $$5$ and $$6$ both contain a

positive integer, what will be the sign of the result in $$4?$