Question

Using the given state table, determine the states that are equivalent. Use an implications table on your evidence.

NS output
PS x=0 x=1 x=0 x=1
a f c 0 0
b d f 0 1
c f b 1 1
d e a 1 0
e e a 1 0
f e c 0 0
g a b 1 1
There may be more than one correct answer.
a). there are no equivalent states
b). a and c
c). c and f
d). b , c and f
e). c and g
f.) a , e and f

Answer 1

To determine equivalent states, create an implications table using the given state table. States c and f are equivalent.

Step-by-step explanation:

To determine the equivalent states, we need to create an implications table using the given state table. Let's label the states as a, b, c, d, e, f, and g. Starting with state a, we can see from the state table that whenever x=0 in state a, we transition to state f. So, we write a ➡️ f. We repeat this process for each state and input combination, filling in the implications table. Once we have the complete implications table, we look for states that have the same implications for all inputs. In this case, states c and f have the same implications for all inputs, so they are equivalent. Therefore, the correct answer is (c) and (f).