Up/Down Counter: Timing Analysis for DOWN Mode
Bidirectional counters in hardware rely on mode-select logic that often introduces asymmetric timing paths between counting up and counting down.
The schematic shows a 4-bit synchronous Up/Down counter built with T flip-flops T0 through T3. The flip-flops only output the non-inverted signal Q. To count down, the borrow chain requires the inverted state Q_bar. The critical path to T3 in UP mode consists of the clock-to-Q delay t_pcq, three cascaded AND gates, and the setup time t_setup. In DOWN mode, the mode-select logic places three cascaded NOT gates into the borrow chain path before the three AND gates.
The timing characteristics are: t_pcq is 2.0ns, t_setup is 2.0ns, AND gate delay t_AND2 is 1.0ns, and NOT gate delay t_NOT is 0.5ns.
Calculate the critical path delay for both UP and DOWN modes and determine the maximum safe clock frequency for the complete bidirectional design.
Constraints
t_pcq= 2.0nst_setup= 2.0nst_AND2= 1.0nst_NOT= 0.5ns- Interconnect routing delay is assumed to be 0ns.
Topics
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