Problem:
An eight-bit binary ripple UP counter with a modulus of 256 is holding the count 01111111. What will be the count after 135 clock pulses?

Solution:
To solve this problem, we need to understand how a binary ripple UP counter works and then calculate the count after 135 clock pulses.

Binary Ripple UP Counter:
A binary ripple UP counter is a type of counter that increments its count value by 1 for each clock pulse. It has multiple flip-flops connected in a cascade configuration, where the output of each flip-flop is connected to the clock input of the next flip-flop. In this type of counter, the least significant bit (LSB) changes its state on every clock pulse, while the most significant bit (MSB) changes its state only when all the lower-order bits are at their maximum count value.

Modulus of 256:
The modulus of a counter represents the total number of unique count values it can hold before resetting to zero. In this case, the modulus is 256, meaning the counter can hold values from 00000000 to 11111111 (0 to 255 in decimal) before resetting.

Given Count:
The given count is 01111111, which represents the decimal value 127. This means that the counter is currently at the count of 127.

Calculating the Count after 135 Clock Pulses:
To calculate the count after 135 clock pulses, we need to determine the count value that will result from incrementing the current count by 135.

Method 1: Direct Calculation:
Since the modulus of the counter is 256, we can directly add 135 to the current count and take the result modulo 256 to obtain the final count.

Current count: 127
Increment by: 135
New count: (127 + 135) % 256 = 262 % 256 = 6

Therefore, the count after 135 clock pulses will be 00000110, which is equivalent to the decimal value 6.

Method 2: Counting Clock Pulses:
Alternatively, we can simulate the counting process by incrementing the count for each clock pulse until we reach 135 pulses.

Starting from the given count 01111111, the next count will be 10000000 (128 in decimal) after one clock pulse. Each subsequent clock pulse will increment the count by 1.

After 135 clock pulses, the count will be:
10000000 + 135 = 10100111

Converting this binary representation to decimal, we get:
10100111 = 1 * 2^7 + 0 * 2^6 + 1 * 2^5 + 0 * 2^4 + 0 * 2^3 + 1 * 2^2 + 1 * 2^1 + 1 * 2^0
= 128 + 0 + 32 + 0 + 0 + 4 + 2 + 1
= 167

Therefore, the count after 135 clock pulses will be 10100111, which is equivalent to the decimal value 167.

Conclusion:
The correct answer is option 'C' (00000110). The count after