If we had to find a representation for the 8 notes in a major music scale (Do-Re-Mi-Fa-Sol-La-Ti-Do, or C-D-E-F-G-A-B-C), we could use 3 binary digits. The pattern 000 could represent C, 001 could represent D, 010 could represent E, and so on. Hence, to represent the phrase "C-D-E-C-E-C-E", we could use 000,001,010,000,010,000,010. This type of encoding is done in modern piano players for representing music digitally. To play music, these types of players have a decoder circuit that can decode the binary representation of the piece of music to be played. The electronic signals corresponding to the notes that are to be 'played' can then be transmitted to a speaker.
In this problem, you will design a decoder circuit that can be used by a digital piano player. The decoder circuit should take a binbary number as input and turn 'on' binary number that was input. For instance, if the input is 011, the circuit should turn on the note for F. Similarly, at the next time step, if the input changes to 010, the circuit should turn off the note for F, and play the note for E instead. The only output that should be 'on' is the one that makes the piano play the appropriate note (i.e., E and F should not be 'on' at the same time).
A) How many input bits will this decoder require? How man output bits will this decoder produce?
B) Draw the truth table for this decoder.
C) Design a circuit for this decoder.