Worked Examples and Waveforms

This supplemental lesson extends number systems with worked examples with expected waveforms. Study it after the core sub-lessons in this topic.

Section context: foundations. Use the diagrams, code, and exercises below together with the main lessons — they are not optional fluff; they mirror what senior engineers attach to block delivery packages.

Learning objectives

• Reproduce the worked example without looking at the solution

• Explain one failure mode and how your TB catches it

• State one timing or protocol assumption explicitly

• Document one integration dependency on other blocks

Quick reference diagram

TOPIC: number-systems
LESSON: Worked Examples and Waveforms
FLOW: spec → RTL → TB → lint → review → merge

Deep dive

This lesson deepens Worked Examples and Waveforms within foundations. Senior reviewers expect you to connect mechanism to HDL fluency, width, and simulation habits — not just define terms.

Start from the spec invariant: what must always be true each cycle? Write it as a Boolean relation, timing budget, or protocol rule before coding. That invariant becomes your reference model, assertion, or waveform check.

At tape-out quality, every block needs a sign-off story: lint clean, self-checking TB, width documented. Treat this lesson as building one paragraph of that story for your project documentation.

Architecture and signal flow

WORKED EXAMPLES AND WAVEFORMS

  inputs ──► [foundations] ──► mechanism ──► outputs
                │                │
           number-systems     verify in sim + lint

Worked example (Verilog/SystemVerilog)

Synthesizable pattern for this topic — simulate locally and compare against your reference.

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logic signed [7:0] a, b;
logic signed [8:0] sum_wide;
assign sum_wide = a + b;
wire ovf = (a[7]==b[7]) && (sum_wide[7]!=a[7]);

Step-by-step design procedure

1. Write the spec invariant (truth table, timing, or protocol rule).

2. Sketch block diagram — inputs, outputs, clock/reset domains.

3. Code the minimal correct version (no optimizations yet).

4. Run self-checking TB with corners: min, max, reset, idle.

5. Lint and review: width, latch, clock, CDC if applicable.

6. Iterate for timing/area only after functionally proven.

Timing and resource trade-offs

METRIC          TYPICAL LEVER
Logic levels      algebra / pipelining
Register count    retiming / sharing
Wire fanout       duplication / pipeline
Power             clock gating / operand isolation
Debug visibility  status flags / SVA / waveform probes

Debug checklist

• Compare DUT vs reference on every stimulus vector

• Capture first cycle of mismatch — not last

• Log seed and plusargs for random regressions

• Check reset release and clock alignment in TB

• If waveform is ambiguous, add temporary assertions

Interview angle

Explain blocking vs non-blocking with a flop example.

MODEL ANSWER SKELETON
1. MECHANISM — one-sentence technical truth
2. MOTIVATION — why this structure vs alternatives
3. WHEN TO USE / SKIP — scope and assumptions
4. PITFALL — common junior mistake
5. EXAMPLE — Verilog or waveform scenario

Practice exercise

Extend the worked example for "Worked Examples and Waveforms": add one corner case, write a self-checking test, and document one intentional pitfall you avoided. Timebox: 30–45 minutes.

Key takeaways

• Connect Worked Examples and Waveforms to HDL fluency, width, and simulation habits.

• Spec → diagram → code → TB → lint is the default loop.

• Document assumptions at block boundaries (width, signedness, latency).

• Interview answers need mechanism + trade-off + example.

Common pitfalls

• Skipping reference model — passes wrong together with DUT.

• Optimizing before correct — ECO cost goes up 10×.

• Ignoring tool warnings — lint/CDC/STA warnings are technical debt.

• Undocumented clock/reset domain — integration surprises.

Extended design scenario

Scenario for Worked Examples and Waveforms: Lint reports latch — find incomplete case in always_comb; add defaults and re-run.

Scenario resolution outline

1. Reproduce with minimal TB — one stimulus, one check.

2. Isolate failing cone (logic, FSM state, or bus beat).

3. Fix root cause — not symptom — in RTL or TB alignment.

4. Add regression test that fails without the fix.

5. Document invariant in comment or SVA for permanence.

Additional simulation pattern

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// Corner-case TB fragment
initial begin
  for (int i = 0; i < 256; i++) begin
    drive(i[7:0]);
    @(posedge clk);
    check(ref(i[7:0]), dut_out);
  end
end

Synthesis and sign-off notes

• Elaborate clean — no OOM from unconstrained generate

• Constraints cover all clocks and I/O delays

• Cross-check RTL parameters vs integration top

• Attach sim log + seed to code review

Lab exercise (45–60 min)

Implement or extend the worked example for "Worked Examples and Waveforms". Add two new test vectors that target different branches. Write a one-paragraph sign-off note covering function, corners, and what you would still verify in SoC context.

Further reading in this course

Next topics in Part: follow nav_order in sidebar.
Cross-part: timing ↔ sequential, CDC ↔ senior interview,
combinational ↔ foundations number systems.

Extended theory

Foundations are the compression algorithm for the rest of the course: every multi-bit bus, FSM output, and STA report ultimately rests on whether you sized, signed, and simulated the bit-level behavior correctly.

For "Worked Examples and Waveforms", the invariant you defend in review is: behavior matches spec under all legal input sequences, reset flows, and backpressure patterns—not just the happy path shown in introductory diagrams.

Write the invariant as a comment above the module or as an SVA property when possible. Future you (and formal tools) will treat it as the contract.

Waveform reading guide

WAVEFORM NARRATIVE — Worked Examples and Waveforms

cycle 0: reset asserted, outputs safe/idle
cycle 1-2: reset held, clocks running
cycle 3: reset released, first legal inputs
cycle 4+: check output latency (N cycles)
mark FIRST mismatch cycle — not last

Second worked example

Alternate pattern emphasizing debug, coverage, or integration:

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// Self-checking scoreboard pattern
class Scoreboard;
  int err;
  function void check(string name, logic [31:0] exp, act);
    if (exp !== act) begin
      $error("%s exp=%h act=%h", name, exp, act);
      err++;
    end
  endfunction
endclass

Comparison: naive vs production

NAIVE APPROACH              PRODUCTION APPROACH
quick hack, one sim vector    self-checking TB + corners
ignore lint warnings          zero new waivers
implicit widths               explicit casts/parameters
undocumented latency          latency in module header comment

Additional interview questions

• Explain Worked Examples and Waveforms to a verification engineer — what would they assert?

• What breaks first at high frequency or low voltage?

• What is your rollback plan if synthesis QoR is unacceptable?

• How would you debug this block with only a 32-bit GPIO trace?

Follow-up interview model answer

Q: What is the #1 mistake with Worked Examples and Waveforms?
A:
  MECHANISM: [core rule in one line]
  MOTIVATION: why teams care in tape-out
  PITFALL: what juniors do wrong
  EXAMPLE: one Verilog line or one waveform event

Hands-on lab part 2

1. Fork the worked example; add one assertion or SVA cover.

2. Inject a bug deliberately; confirm TB or assertion catches it.

3. Write 5-bullet PR description for your change.

4. Peer review: can a teammate enable the block without asking you?

Sign-off evidence checklist

• Directed sim log attached (PASS, seed noted)

• Lint report clean for touched files

• If sequential: reset + clocking section in README

• If bus-facing: protocol cheat sheet in module doc

• If timing-critical: note expected critical path endpoint