Explanation:

Introduction
In digital electronics, a counter is a sequential circuit that is used to count the number of occurrences of an event. Counters are widely used in various applications such as frequency division, timekeeping, and digital signal processing.

MOD Counter
A MOD counter is a type of counter where the number of states or counts is equal to the modulus of the counter. The modulus of a counter represents the number of different states it can have before it overflows and resets back to zero.

MOD-2 Up-Counter
A MOD-2 up-counter is a counter that counts in binary and has a modulus of 2. It means that it can have two states: 0 and 1. When the counter reaches its maximum count (1), it resets back to 0 and starts counting again.

MOD-5 Up-Counter
A MOD-5 up-counter is a counter that counts in binary and has a modulus of 5. It means that it can have five different states: 0, 1, 2, 3, and 4. When the counter reaches its maximum count (4), it resets back to 0 and starts counting again.

Cascading the MOD-2 and MOD-5 Up-Counters
When a MOD-2 up-counter and a MOD-5 up-counter are cascaded together, the output of the MOD-2 counter is connected to the clock input of the MOD-5 counter. This means that for every two clock cycles of the MOD-2 counter, the MOD-5 counter will increment by one.

Explanation of Counts
Let's analyze the counts of the cascaded MOD-2 and MOD-5 up-counters.

- Initially, both counters are at their minimum count values: MOD-2 counter = 0, MOD-5 counter = 0.
- After the first clock cycle, the MOD-2 counter increments to 1, but the MOD-5 counter remains at 0.
- After the second clock cycle, the MOD-2 counter resets back to 0, and the MOD-5 counter increments to 1.
- After the third clock cycle, the MOD-2 counter increments to 1 again, but the MOD-5 counter remains at 1.
- After the fourth clock cycle, the MOD-2 counter resets back to 0, and the MOD-5 counter increments to 2.
- This pattern continues until the MOD-5 counter reaches its maximum count of 4. At this point, the MOD-2 counter has cycled twice: 0 -> 1 -> 0 -> 1.
- After the tenth clock cycle, the MOD-2 counter will be at its maximum count of 1, and the MOD-5 counter will be at its maximum count of 4. The counters will reset back to their minimum counts: MOD-2 counter = 0, MOD-5 counter = 0.

Conclusion
Therefore, when a MOD-2 and a MOD-5 up-counter are cascaded together, the combined counter will have a modulus of 10. It means that the counter will have ten different states: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. After