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 processor with $$64$$ registers and an instruction set of size twelve. Each instruction has five distinct fields, namely, opcode, two source register identifiers, one destination register identifier, and a twelve-bit immediate value. Each instruction must be stored in memory in a byte-aligned fashion. If a program has $$100$$ instructions, the amount of memory (in bytes) consumed by the program text is _____________.

The width of the physical address on a machine is $$40$$ bits. The width of the tag field in a $$512$$ $$KB$$ $$8$$-way set associative cache is _____________ bits.

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.