Question

A MOD 2 and a MOD 5 up-counter when cascaded together results in a MOD ________ counter. (in integer)

Hint:

To find the total MOD value when cascading counters, multiply the MOD values of the individual counters. This is applicable in most digital counter designs.

Answer 1

Correct Answer: 10

When two counters are cascaded together, the overall MOD value is simply the product of the MOD values of the individual counters. This principle is fundamental when working with counters in digital circuits, as it ensures that both counters must complete their counting cycles before the system can reset.
The MOD value for a counter indicates the number of distinct states it can go through before resetting. For example: - A MOD 2 counter counts from 0 to 1, so it has 2 states.
- A MOD 5 counter counts from 0 to 4, so it has 5 states.
When these two counters are connected in cascade (one after the other), each counter will trigger the next one after completing its own cycle. Therefore, the total number of unique states in the system is the product of the individual MOD values.
For this question, the MOD value for the first counter is 2, and for the second counter, it is 5. The total MOD value of the cascaded system is: \[ \text{MOD} = 2 \times 5 = 10. \] Thus, the total number of distinct states or the MOD value for the cascaded counters is \( \boxed{10} \).