Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Digital systems, linear algebra, introduction to formal proof / 3 / e

The likely effect in a single-cycle or unchanged pipeline-stage implementation is a longer combinational critical path and hence a lower maximum processor clock frequency. Previously the barrel shifter and ALU could work in parallel before result selection; the modified path can require both shift and addition before address or result use.

Ignoring common processor register and wiring delays, the relevant combinational logic contribution changes roughly from $\max (t_{\mathrm{ALU}},t_{\mathrm{shift}})+t_{\mathrm{mux}}$ to $t_{\mathrm{shift}}+t_{\mathrm{ALU}}$, with any additional input selection included as needed. The processor clock period must also cover processor register timing and the rest of the instruction path, potentially including memory access. Removing a multiplexer offsets some delay, so a numerical frequency change cannot be inferred without component timings. Pipelining, a faster implementation or another pre-existing bottleneck can alter the outcome; the changed serial dependence is the reason for the likely reduction.