Consider the following processors ($$ns$$ stands for nanoseconds). Assume that the pipeline registers have zero latency.
$$P1:$$ Four-stage pipeline with stage latencies $$1$$ $$ns,$$ $$2$$ $$ns,$$ $$2$$ $$ns,$$ $$1$$ $$ns.$$
$$P2:$$ Four-stage pipeline with stage latencies $$1$$ $$ns,$$ 1$$.5$$ $$ns,$$ $$1.5$$ $$ns,$$ $$1.5$$ $$ns.$$
$$P3:$$ Five-stage pipeline with stage latencies $$0.5$$ $$ns,$$ $$1$$ $$ns,$$ $$1$$ $$ns,$$ $$0.6$$ $$ns,$$ $$1$$ $$ns.$$
$$P4:$$ Five-stage pipeline with stage latencies $$0.5$$ $$ns,$$ $$0.5$$ $$ns,$$ $$1$$ $$ns,$$ $$1$$ $$ns,$$ $$1.1$$ $$ns.$$

Which processor has the highest peak clock frequency?

Consider an instruction pipeline with five stages without any branch prediction: Fetch Instruction $$(FI),$$ Decode Instruction $$(DI),$$ Fetch Operand $$(FO),$$ Execute Instruction $$(EI)$$ and Write Operand $$(WO).$$ The stage delays for $$FI, DI, FO, EI$$ and $$WO$$ are $$5$$ $$ns,$$ $$7$$ $$ns,$$ $$10$$ $$ns,$$ $$8$$ $$ns$$ and $$6$$ $$ns$$, respectively. There are intermediate storage buffers after each stage and the delay of each buffer is $$1$$ $$ns.$$ A program consisting of $$12$$ instructions $${{\rm I}_1},{{\rm I}_2},{{\rm I}_3},......,\,\,{{\rm I}_{12}}$$ is executed in this pipelined processor. Instruction $${{\rm I}_4}$$ is the only branch instruction and its branch target is $${{\rm I}_9}$$. If the branch is taken during the execution of this program, the time (in $$ns$$) needed to complete the program is

Consider an instruction pipeline with four stages $$\left( {S1,\,S2,\,S3,} \right.$$ and $$\left. {S4} \right)$$ each with combinational circuit only. The pipeline registers are required between each stage and at the end of the last stage. Delays for the stages and for the pipeline registers are as given in the figure.

What is the approximate speed up of the pipeline in steady state under ideal conditions when compared to the corresponding non-pipeline implementation?

A $$5$$-stage pipelined processor has Instruction Fetch $$(IF),$$ Instruction Decode $$(ID),$$ Operand Fetch $$(OF),$$ Perform Operation $$(PO)$$ and Write Operand $$(WO)$$ stages. The $$IF, ID, OF$$ and $$WO$$ stages take $$1$$ clock cycle each for any instruction. The $$PO$$ stage takes $$1$$ clock cycle for $$ADD$$ and $$SUB$$ instructions, $$3$$ clock cycles for $$MUL$$ instruction, and $$6$$ clock cycles for $$DIV$$ instruction respectively. Operand forwarding is used in the pipeline. What is the number of clock cycles needed to execute the following sequence of instructions?