VLSI DV Interview Puzzles · All levels

Boolean dist Cascading into Value dist

Compute P(code==0) and P(code==501).

Puzzle

Difficulty: Medium · Puzzle 5 of 6 · Topic: Distribution Puzzles (`dist`, `:=` vs `:/`)

Compute P(code==0) and P(code==501).

Code

systemverilog

class err_code;
  rand bit is_err;
  rand int unsigned code;
  constraint c_prob { is_err dist {0 := 9, 1 := 1}; }
  constraint c_map {
    if (is_err) code dist { [500:503] :/ 4 };
    else        code == 0;
  }
endclass

Hint

Use conditional probability: P(code=v)=P(branch)*P(v|branch).

Step-by-step solution

diagram

1) P(is_err=1)=1/10 and P(is_err=0)=9/10 from c_prob.
2) If is_err=0, code is deterministically 0.
3) If is_err=1, [500:503] :/ 4 makes each of 500..503 equal at 1/4.
4) Therefore P(code=0)=9/10.
5) P(code=501)= (1/10)*(1/4)=1/40.

Answer

Answer: P(code==0)=90% and each error code 500..503 is 2.5% (including 501).

Why candidates get it wrong

Candidates often compute 1/4 for code 501 and forget the branch probability multiplier.

Interviewer follow-up

How would you make all five outcomes {0,500,501,502,503} exactly uniform?

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