A barrel shifter is a digital subsystem that can shift multiple bits in a vectors
positions at once. In a single pass through the shifter, the input can rotate
from 0 to 7 positions. Barrel shifters are useful for implementing bit extraction
operations supported in many computer instruction sets. The subsystem has
eight data inputs, D7, D6, , D0, eight data outputs, O7, O6, …,O0, and three
control inputs, S2, S1, S0. The control inputs specify the number of positions to
shift the input to the left. Inputs that "fall off the end" are rotated around to the
low-order bits of the output. For example, when S2 = S1 = S0 = 0, the inputs
are simply gated straight through to the outputs: O7 = D7, O6 = D6, , O1 = D1,
O0 = D0. When S2 = S1 = 0, S0 = 1, the input bits are shifted one place toward
the left: O7 = D6, O6 = D5, …, O1 = D0, O0 = D7. Note that D7 is rotated around
to the 0th output position. When S2 = S1 = S0 = 1, the input is shifted seven
positions to the left, with the high-order bits wrapping around to the low-order
output positions: O7 = D0, O6 = D7, …, O1 = D2, O0 = D1. This is the same as
shifting one position to the right, with the inputs wrapping from the low-order to
the high-order positions. Write the truth table for the 8-bit barrel shifter with the
bit positions determined by the value of the three control signals.