Given information:
- 4-bit preset table UP counter
- Preset input: 0111
- Preset operation takes place as soon as the counter becomes maximum (1111)

To find: Modulus of the counter

Solution:
1. Understanding the operation of a preset table UP counter:
- A preset table UP counter is a type of digital counter that increments its count by 1 for every clock pulse.
- It has an additional input called "preset" that allows the counter to be loaded with a specific count value.
- When the preset input is activated, the counter will load the pre-determined count value instead of counting up from its current state.
- In this case, the preset input is set to 0111.

2. Counting sequence of the UP counter:
- The counter starts from 0000 and counts up to 1111 in binary.
- After reaching 1111, the next clock pulse will reset the counter to 0000 and the counting sequence will start again.

3. Preset operation of the UP counter:
- As per the given information, the preset operation takes place as soon as the counter becomes maximum (1111).
- When the counter reaches 1111, the preset input will load the pre-determined count value of 0111.
- Therefore, the next count value will be 1000 instead of 0000.

4. Modulus of the UP counter:
- The modulus of a counter is the number of unique count values it can generate before repeating the counting sequence.
- In this case, the counter has 4 bits and can generate a total of 2^4 = 16 unique count values.
- However, since the preset operation changes the counting sequence after reaching 1111, the modulus of the counter will be reduced to 8.
- Therefore, the modulus of this counter is 8.

Answer: The modulus of the 4-bit preset table UP counter with preset input 0111 is 8.