Design an arithmetic shifter. The device should input a 4-bit value x and a 2-bit control c and output a 4-bit value representing the shifted input. If c = 00 then shift left one, if c = 01 then shift right one, if c = 10 then shift right two, and when c = 11 output x without shift.
For an example of how this works, consider the possible inputs x1 = 1011 and x2 = 0111. When we shift left we fill in the 0's so that a shift of one left gives x1 = 0110 and x2 = 1110. When we shift right we fill with the sign bit, so that a shift of one right gives x1 = 1011 and x2 = 0011 and a shift of two right gives x1 = 1110 and x2 = 0001.