The number of flip-flops required to design a modulo - 272 counter is:*8

To design a modulo-272 counter, we need to determine the number of flip-flops required.

Step 1: The first step is to understand what a modulo-272 counter is. A modulo-272 counter is a counter that counts from 0 to 271 (272 states in total) and then resets back to 0.

Step 2: The number of flip-flops required for a counter is determined by the number of states the counter has. This is because each flip-flop represents a binary digit or bit, and the number of bits required is determined by the highest number the counter needs to count to.

Step 3: To find out how many bits are needed to represent 272 states, we can use the formula 2^n >= 272, where n is the number of bits. We need to find the smallest value of n that satisfies this equation.

Step 4: If we start with n=1, 2^1 = 2, which is less than 272. If we try n=2, 2^2 = 4, which is still less than 272. We continue this process until we find a value of n where 2^n is equal to or greater than 272.

Step 5: When we reach n=9, 2^9 = 512, which is greater than 272. Therefore, we need 9 flip-flops to design a modulo-272 counter.

So, the number of flip-flops required to design a modulo-272 counter is 9, not 8.