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Counting in Reverse

Now that we've seen normal counting, let's see how we can count backwards. Countdowns are required in a wide range of applications, including everyday tasks. Remaining cooking time for either a conventional oven or microwave oven is commonly displayed this way, as distinguished from the time display that shows when the oven isn't doing something else.

Here we will modify the standard ripple counter to make it count backwards instead.

 In the 4-bit counter to the right, we are still using edge-triggered master-slave flip-flops similar to those in the Sequential portion of these pages. The output of each flip-flop changes state on the falling edge (1-to-0 transistion) of the T input. However, note that in this case each T input is triggered by the Q' output of the prior flip-flop, rather than by the Q output. As a result, each flip-flop will change state when the prior one changes from 0 to 1 at its Q output, rather than changing from 1 to 0. Because of this, the first pulse will cause the counter to change state from 0000 to 1111.    Since this circuit counts downwards instead of upwards, we are left with a possible question: if the initial state of all zeroes represents a count of zero, what is the value represented by the next state of all ones? Is it 15 this time? Or would it be more true to call this state -1 for this circuit?

This in turn leads us to an essential question: how can we deal with negative numbers in binary notation? We must be able to do it, since negative numbers have meaning and must be dealt with mathematically.

Since negative numbers fall in the province of mathematical computation, we deal with them in their own page, on Negative Numbers and Binary Subtraction.

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