A production plant has a requirement for a counter that will count 4,000 items before recycling and starting over. How many D flip-flop stages would be required in this counter

12

Explanation:

A n-bit integer represents values from 0 to (2^n) - 1 states. For example, if we have 3 bits we can count up to 7 states, that is counting from 0 to 7.

On the other hand, a flip flop stores one bit of data So, we will need n flip flops to count (2^n) - 1 states.

So we have production plant that requires a counter that will count 4,000 items before recycling and starting over.

Therefore (2^n) - 1 = 4000. The nearest integer value of n that will give 4000 is 12.

For n = 12, 2^12 = 4096 and for n = 11 2^11 = 2048. 12 is the closest value. Therefore we need 12 D Flip Flop stages to count the required items.