A processor has $$16$$ integer registers $$\left( {R0,\,\,R1,\,\,..\,\,,\,\,R15} \right)$$) and $$64$$ floating point registers $$(F0, F1,… , F63).$$ It uses a $$2$$-byte instruction format. There are four categories of instructions: Type-$$1,$$ Type-$$2,$$ Type-3, and Type-$$4.$$ Type-$$1$$ category consists of four instructions, each with $$3$$ integer register operands $$(3Rs)$$. Type-$$2$$ category consists of eight instructions, each with $$2$$ floating point register operands $$(2Fs).$$ Type-$$3$$ category consists of fourteen instructions, each with one integer register operand and one floating point register operand $$(1R+1F).$$ Type-$$4$$ category consists of $$N$$ instructions, each with a floating point register operand $$(1F).$$

The maximum value of $$N$$ is __________.

Consider the following processor design characteristics.

$$\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,$$ Register-to-register arithmetic operations only
$$\,\,\,\,\,{\rm I}{\rm I}.\,\,\,\,\,$$ Fixed-length instruction format
$$\,\,\,{\rm I}{\rm I}{\rm I}.\,\,\,\,\,$$ Hardwired control unit

Which of the characteristics above are used in the design of a $$RISC$$ processor?

The following are some events that occur after a device controller issues an interrupt while process $$L$$ is under execution.

$$(P)$$ The processor pushes the process status of $$L$$ onto the control stack.
$$(Q)$$ The processor finishes the execution of the current instruction.
$$(R)$$ The processor executes the interrupt service routine.
$$(S)$$ The processor pops the process status of $$L$$ from the control stack.
$$(T)$$ The processor loads the new PC value based on the interrupt.

Which one of the following is the correct order in which the events above occur?

Let $$G$$ be a simple undirected graph. Let $${T_D}$$ be a depth first search tree of $$G.$$ Let $${T_B}$$ be a breadth first search tree of $$G.$$ Consider the following statements.

$$(I)$$ No edge of $$G$$ is a cross edge with respect to $${T_D}.$$ ($$A$$ cross edge in $$G$$ is between
$$\,\,\,\,\,\,\,\,$$ two nodes neither of which is an ancestor of the other in $${T_D}.$$)
$$(II)$$ For every edge $$(u,v)$$ of $$G,$$ if $$u$$ is at depth $$i$$ and $$v$$ is at depth $$j$$ in $${T_B}$$, then
$$\,\,\,\,\,\,\,\,\,\,\,$$ $$\left| {i - j} \right| = 1.$$

Which of the statements above must necessarily be true?