Suppose the functions $$F$$ and $$G$$ can be computed in $$5$$ and $$3$$ nanoseconds by functional units $${U_F}$$ and $${U_G},$$ respectively. Given two instances of $${U_F}$$ and two instances of $${U_G},$$ it is required to implement the computation $$F\left( {G\left( {{X_i}} \right)} \right)$$ for $$1 \le i \le 10.$$ Ignoring all other delays, the minimum time required to complete this computation is _____________ nanoseconds.

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_________.