30Implementation

Count set bits with control flow

Situation and starter reading

countOnes must return the number of set bits in an eight-bit input. The starter compiles, but the function initializes count and immediately returns it without reading value.

Read the function signature first: a four-bit result can represent every count from zero through eight. Then read the three calls in mkTop; they exercise a mixed byte, an all-one byte, and an all-zero byte. Edit only the body of countOnes. Treat its signature and the observation rule in mkTop as fixed.

Predict before editing

Run the starter mentally before pressing Run. Since no expression depends on value, all three calls report zero. Compilation succeeds because the code is type-correct; this is a behavioral defect, not a syntax or type error.

For the repair, maintain this invariant: after processing index i, count equals the number of one bits seen from index 0 through i. A constant-bounded loop controls how much logic is generated, while the if tests runtime input. The accumulator uses local = assignment, so the function remains combinational rather than becoming an eight-cycle machine.

Required change and observable completion

• Examine exactly indices 0 through 7 with an Integer loop variable and constant bounds.
• Increase count only when the selected bit is one.
• Preserve the function signature and surrounding module.

Run is observably correct when the mixed sample reports five, the all-one sample reports eight, and the all-zero sample remains zero. The implementation must also work for other bit patterns; hard-coding those three results does not satisfy the function contract.

Progressive hints

Transfer experiment

After completion, temporarily invert the tested condition so the same loop counts zero bits. Predict the new three results and explain why each new count plus the original count equals eight. Restore the set-bit version afterward.