Consider the following network (called a butterfly network), where the Ai represent incoming data and the Bi the outgoing data. Assume that each switch works as specified in part (a). Assume that each switch has a separate control line and that these control lines are specified r.c where r is the row (numbered 0 to 3 from the top) and c is the column (numbered 0 to 2, left to right).

Give switch settings that would route A0 to B5, leaving unspecified any switches that are not needed.

Give switch settings that would route A6 to B0.

Can every input be connected to every output?

Give routings for two A inputs to two B outputs that are incompatible (cannot be satisfied at the same time).

B0 B1 B2 B3 B4 B5 B6 B7 5 6 B0 B1 B2 B3 B4 B5 B6 B7 5 6