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A2 Flow Table Reduction

# A2 Flow Table Reduction - Lets start with the state table...

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Let’s start with the state table for the more stringent interpretation of the specification. 00 01 11 10 1 1 / 0 2 / - - / - 3 / - 2 1 / - 2 / 0 4 / - - / - 3 5 / - - / - 6 / - 3 / 1 4 - / - 2 / - 4 / 0 7 / - 5 5 / 1 8 / - - / - 3 / - 6 - / - 8 / - 6 / 0 9 / - 7 1 / - - / - 4 / - 7 / 0 8 10 / - 8 / 0 6 / - - / - 9 10 / - - / - 6 / - 9 / 0 10 10 / 0 8 / - - / - 9 / - We’re going to try reducing this using the two-step method. Remember that step 1 of the two-step method involves determining whether any of the states of the table are equivalent . In order for two states to be equivalent, their next states must be equivalent where both are specified, and their outputs must be the same where both are specified. This requires that two states have all of their don’t cares in the same place which, in general, means that the two states must be stable for the same input. If there are don’t cares that don’t result from the Fundamental Mode assumption, then that must also be taken into consideration. The states that are stable for the same input combination fall into the following sets: {1,5,10};{2,8};{4,6}; {3,7,9}. For each set of states, we will make a mini-implication table that compares only the states in that set. 5 7 10 2,8 3,9 8 1,10 4,6 6 2,8 7,9 9 1,10 4,6 1 5 2 4 3 7 None of the states in the table above are equivalent. This should come as no surprise, since we’ve really already shown that all of the states have represent different pieces of state information. Given that none of these states are equivalent, in step 2 we will check for compatibility among the states.

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