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7 July, 04:20

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

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  1. 7 July, 07:37
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    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.
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