The principle of counting in a 4-bit down counter involves sequentially decrementing values from the maximum count (1111 in binary) to the minimum count (0000 in binary). Each count value is represented by four flip-flops that are connected in a cascading manner, with each flip-flop triggering the next lower-order flip-flop to toggle at the correct time. This creates a sequence of counts where one bit changes at a time, resulting in a downward count.
