PYTHON · NUMPY

The Critical Path

Compute a design's critical-path delay and see why a ripple-carry adder can't hit a fast clock — the timing half of PPA.

01Challenge

Your ripple-carry adder is correct but slow: the carry must ripple through every bit before the answer is valid. Compute its critical-path delay at a real gate speed, find the max clock it can hit, and show a look-ahead structure beats it.

Predict firstAn 8-bit ripple-carry adder gives the right answer. What sets the fastest clock it can run at?

02Model

Correct is not enough — a chip has a clock, and every path from register to register must settle within one tick. The slowest such path is the critical path, and it sets the maximum frequency. In a ripple-carry adder the carry chain is the critical path: delay grows linearly with width, so a wide ripple adder is slow. Carry-lookahead computes carries in parallel, cutting the delay from about 2N gate-delays to roughly log N — the same trade every real datapath makes: more gates (area) to buy speed.

03Guided practice

Worked: model ripple delay as ~2N gate-delays. Faded: convert to nanoseconds and a max frequency. Independent: compare against a log-depth lookahead and check it meets 1 GHz.

04Feedback

PASS WHEN You found the critical path, turned it into a clock ceiling, and showed how a faster structure clears it — real timing closure in miniature.

If your run fails, check:

FAIL: check the delay model — ripple is ~2N gate-delays, lookahead ~log-depth.
FAIL: units — max frequency is 1 divided by the critical-path time in nanoseconds.

05Retrieve & space

What sets a chip's maximum clock? (The critical path — the slowest register-to-register delay.)
Why is ripple-carry slow? (Its carry chain delay grows linearly with bit width.)
What does carry-lookahead spend to go faster? (More gates — area — to shorten the path.)

06Mastery & project

Computes critical-path delay and max frequency and contrasts linear vs log-depth structures (L3: timing analysis and the area-speed trade).

Area (last lesson) plus timing (this one) is PPA — the scorecard every accelerator in Module 3 is judged on.

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PYTHON · NUMPY

The Critical Path

Compute critical-path delay and max clock for ripple vs carry-lookahead.

You read

the arrays and values already in scope

You change

the code you write in each cell

Fixed

the dataset and the checks that grade you