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?

Consider a $$4$$ stage pipeline processor. The number of cycles needed by the four instructions $${\rm I}1,$$ $${\rm I}2,$$ $${\rm I}3,$$ $${\rm I}4,$$ in stages $$S1, S2, S3, S4$$ is shown below.

What is the number of cycles needed to execute the following loop?
For $$\left( {i = 1} \right.$$ to $$\left. 2 \right)$$ $$\left\{ {{\rm I}1;{\rm I}2;{\rm I}3;{\rm I}4;} \right\}$$

The following code is to run on a pipelined processor with one branch delay slot
$$\eqalign{ & {{\rm I}_1}:\,\,ADD\,\,{R_2}\,\, \leftarrow \,\,{R_7} + {R_8} \cr & {{\rm I}_2}:\,\,SUB\,\,\,{R_4}\,\, \leftarrow \,\,{R_5} - {R_6} \cr & {{\rm I}_3}:\,\,ADD\,\,{R_1}\,\, \leftarrow \,\,{R_2} + {R_3} \cr & {{\rm I}_4}:\,\,STORE\,\,Memory\,\,\left[ {{R_4}} \right]\,\, \leftarrow \,\,{R_1} \cr & BRANCH\,\,to\,\,Label\,\,if\,\,{R_1} = = 0 \cr} $$

Which of the instructions $${{\rm I}_1},\,{{\rm I}_2},\,{{\rm I}_3}$$ or $${{\rm I}_4}$$ can legitimately occupy the delay slot without any other program modification?