05Verification

Match a mask literal to its width

Problem

lowNibbleOf should keep the low four bits of an eight-bit input and clear the other four. The starter already performs the right operation, but its mask is a fill literal. In a Bit#(8) declaration, '1 fills all eight positions with ones, so the AND returns the input unchanged.

Repair the mask literal without changing the function signature or replacing the & expression.

Read and predict

Find the declared type of mask, then use that context to determine the value of '1. Before editing, predict the three visible calls:

8'ha5 remains 8'ha5 instead of becoming 8'h05.
8'hf0 remains 8'hf0 instead of becoming 8'h00.
8'h3c remains 8'h3c instead of becoming 8'h0c.

Run the starter once and compare its trace with those predictions.

Make the smallest change

Replace only the mask literal with a sized hexadecimal literal whose upper four bits are zero and lower four bits are one. Keep mask as Bit#(8) and preserve return value & mask;.

After the change, the result must satisfy both parts of the operation: the high nibble is zero, and the low nibble matches the input.

Check the result

Run the public examples again. They should report:

8'ha5 -> 8'h05
8'hf0 -> 8'h00
8'h3c -> 8'h0c

Explain why the corrected bit pattern fixes the mistake. A sized mask records both the number of bits and their pattern, while a fill literal takes its width from the surrounding type.

Progressive hints

Hint 1

Write the eight mask bits in two groups of four. Which group must be zero, and which group must be one?

Hint 2

Use an eight-bit hexadecimal literal so that the source states the mask width rather than relying on contextual filling.

Concept

A fill literal has no independent width. Context turns '1 into an all-ones value of the required size; here that is 8'hff, which cannot clear any input bit. Sized literals are preferable for fixed masks because their width and bit pattern are visible together.

Variation: keep three bits

After the required version works, temporarily preserve only the low three bits. For the visible 8'h3c input, predict 8'h04, derive the corresponding eight-bit mask, and confirm the result. Restore the low-four-bit mask before submitting.