Answer:
12
Step-by-step 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.