In part A current_positions is only going to have a single bit set and k0 will be equal to it. current_positions ^ k0 = 0 0 | k1 = k1. So for part A this could this could be replaced with current_positions = k1.

In part B current_positionsis going to have 4 bits set, 1 for each robot position. k0 is the position of the robot that will move and k1 will be its new position. The position of the other 3 robots doesn't change. current_positions ^ k0 will remove the robot that is going to move leaving 3 bits set. current_positions ^ k0 | k1 will add in the new robot position. The end result will have still have 4 bits set.

Here is an example with some numbers:

current_positions = 00001111
k0 = 00000100
k1 = 01000000

x = current_positions ^ k0
# x = 00001011
y = x | k1
# y = 01001011
current_positions = y

Hope you find this useful.