25Implementation

Turn a hex digit into its ASCII character

Problem

Intended behavior. HexChar converts a 4-bit digit into the ASCII code of its lowercase hexadecimal character. Digits 0 to 9 become '0' to '9' (codes 48 to 57), and 10 to 15 become 'a' to 'f' (codes 97 to 102). ascii is combinational: it follows digit without waiting for a clock edge.

Current behavior. Digits 0 to 9 are already right. For 10 to 15 the starter keeps counting past '9' and produces the punctuation characters that follow it in the ASCII table.

Your task. Change the line under the TODO so that all sixteen digits map correctly. The hardware lives in HexChar. TracedHexChar adds only a printf to the same hardware, and the public run simulates it; keep that class and the ports unchanged.

Read and predict

The printf reports two signals with three format specifiers: digit in hex, ascii as a character, and ascii in decimal. The public bench pokes the digits 0 to 15, one per clock step, and prints nothing itself. Every line of output comes from the circuit.

Before running, predict:

how many lines the run prints, and whether the reset cycle chiseltest runs first adds one;
how the digit= and char= columns relate on every line of a correct converter;
what char= shows for digit 10 in the starter, given that : follows 9 in the ASCII table.

Diagnose

For a correct converter, the hex digit printed by %x and the character printed by %c are the same symbol on every line. The lines where they differ are the inputs still to fix, and the code= column shows how far off each one is. The starter adds one offset, the code of '0', to every digit. Letters need a different offset, because 'a' does not come right after '9' in ASCII.

Completion check

All sixteen digits produce the right code, with lowercase 'a' to 'f', matching what %x prints.
The boundary between the two ranges is exact: 9 still becomes '9', and 10 becomes 'a'.
ascii is right in the same cycle the digit is applied, for inputs in any order.

Hints

Hint 1

Split the digits into two ranges and give each range its own starting character. The trace already shows the first line where the second range goes wrong.

Hint 2

digit is a hardware value, so the choice between the two results needs a hardware selection on a comparison of digit with 10, not a Scala if. In the letter range, digit 10 has to land exactly on the code of 'a'.

Concept

%c turns a number into a character only when it is printed. The hardware carries plain 8-bit codes. Printing %x next to %c lets you compare the symbols on every non-reset edge without working out each expected code by hand. The trace does not assert that they match; you must inspect it.

Variation

Make the letters uppercase. Predict the new code= values for 10 to 15, and explain why the digit= and char= columns stop matching even though the converter is now correct for uppercase.