Consider a $$3$$ $$GHz$$ (gigahertz) processor with a three-stage pipeline and stage latencies $${\tau _1},{\tau _2},$$ and $${\tau _3}$$ such that $${\tau _1} = 3{\tau _2}/4 = 2{\tau _3}.$$ If the longest pipeline stage is split into two pipeline stages of equal latency, the new frequency is ____________ $$GHz,$$ ignoring delays in the pipeline registers.

The stage delays in a $$4$$-stage pipeline are $$800, 500, 400$$ and $$300$$ picoseconds. The first stage (with delay $$800$$ picoseconds) is replaced with a functionally equivalent design involving two stages with respective delays $$600$$ and $$350$$ picoseconds. The throughput increase of the pipeline is percent.

Consider a non-pipelined processor with a clock rate of 2.5 gigahertz and average cycles per instruction of four. The same processor is upgraded to a pipelined processor with five stages; but due to the internal pipeline delay, the clock speed is reduced to 2 gigahertz. Assume that there are no stalls in the pipeline. The speed up achieved in this pipelined processor is_________.

Consider the sequence of machine instructions given below:

MUL	R5, R0, R1
DIV	R6, R2, R3
ADD	R7, R5, R6
SUB	R8, R7, R4

In the above sequence, $$R0$$ to $$R8$$ are general purpose registers. In the instructions shown, the first register stores the result of the operation performed on the second and the third registers. This sequence of instructions is to be executed in a pipelined instruction processor with the following $$4$$ stages: $$(1)$$ Instruction Fetch and Decode $$(IF), (2)$$ Operand Fetch $$(OF), (3)$$ Perform Operation $$(PO)$$ and $$(4)$$ Write back the result $$(WB).$$ The $$IF,$$ $$OF$$ and $$WB$$ stages take $$1$$ clock cycle each for any instruction. The $$PO$$ stage takes $$1$$ clock cycle for $$ADD$$ or $$SUB$$ instruction, $$3$$ clock cycles for $$MUL$$ instruction and $$5$$ clock cycles for $$DIV$$ instruction. The pipelined processor uses operand forwarding from the $$PO$$ stage to the $$OF$$ stage. The number of clock cycles taken for the execution of the above sequence of instructions is _______________________ .