03Verification

Add a signed offset

Problem

Intended behavior. SignedOffset moves an 8-bit address base by a signed 4-bit delta between −8 and 7. addr is base + delta, wrapping within eight bits: 250 + 7 gives 1 and 3 + (-8) gives 251.

Current behavior. The starter compiles and positive offsets work. Every negative offset moves the address forward: 100 + (-1) prints 115.

Task. Find why a negative delta is read as a large positive number and fix the addr connection. Keep all three port types.

Read the starter

The ports already say what each value means: base is unsigned and delta is SInt. Follow delta = -1 through the single connection. Write its four bits, then ask what asUInt turns them into and how the addition widens that 4-bit value to meet the 8-bit base.

Predict before running

The public run prints four rows: (100, 3), (100, -1), (100, -8), and (250, 7). Predict the starter's output for each, then the correct output. Mark which rows the defect touches.

Run and explain

The starter prints 103, 115, 108, and 1. The two positive rows are right, including the wrap at 250. For −1 the bits are 1111; once asUInt reads them as 15, the widening to eight bits pads with zeros, so the sum is 100 + 15. For −8, 1000 becomes 8 and the sum is 108. The bits were never wrong. The reading was changed to unsigned before the value was widened, so the extension used zeros instead of copies of the sign bit. Correct output is 103, 99, 92, and 1.

Completion check

• Every base from 0 to 255 combined with every delta from −8 to 7 gives base + delta modulo 256.
• Wrapping works in both directions, past 255 and below 0.
• Matching the printed offsets alone does not count; −2 through −7 must work too.

Progressive hints

Transfer experiment

Read base = 200 as an 8-bit SInt: it is −56. Explain why doing the addition in signed arithmetic still produces the right unsigned address for 200 + (-8) and for 250 + 7.