LFSR vs. Binary Counter: Timing Advantage Analysis
High-speed digital systems use Linear Feedback Shift Registers (LFSRs) instead of standard binary counters to eliminate deep combinational logic paths.
The schematic shows two 8-bit counters operating side-by-side: a standard synchronous binary counter and a Fibonacci LFSR. The binary counter uses a 3-level AND tree to compute the carry-lookahead signals for its most significant bits. The LFSR uses a single XOR gate in its feedback path to compute the next state. The standard cell library specifies the following timing characteristics: t_pcq = 2.0ns, t_setup = 1.0ns, t_AND = 1.0ns, and t_XOR = 0.5ns.
Analyze the critical path for both architectures. Determine the maximum operating frequency for each 8-bit design and identify the crossover point where the LFSR gains its timing advantage.
Constraints
- Assume interconnect delay is negligible.
- The binary counter's critical path is modeled entirely by the clock-to-q delay, the AND tree delay, and the setup time.
- Clock skew and jitter are assumed to be zero.
- Frequencies must be calculated in MHz and rounded to the nearest whole number.
Topics
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