Final answer:
To construct a counter that follows the sequence 8, 9, ..., 25, 8, 9, ..., 25, etc., you can use a combination of 74LS163 IC counters and a flip-flop.
Step-by-step explanation:
To construct a counter that follows the sequence 8, 9, ..., 25, 8, 9, ..., 25, etc., using a minimum number of 74LS163 IC counters and external logic gates, you can use a combination of 74LS163 IC counters and a flip-flop. Here is a sketch of the circuit:
First, you can use a 4-bit synchronous counter (74LS163) as the main counter. This counter will count from 8 to 15 and then reset to 8. You can use the Q0 output of this counter to trigger a flip-flop, which will count from 0 to 7 and then reset to 0. The outputs of the flip-flop can then be combined with the outputs of the synchronous counter using external logic gates to generate the desired sequence.
By using this combination of the 74LS163 IC counters and external logic gates, you can achieve the desired sequence with a minimum number of components.