M16_2_Discussion6

M16_2_Discussion6 - s 1 (t) = A if x(t - 1) = 3 s 1 (t) = B...

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Exercise 7.22 A sequential system has a decimal digit as input and a radix-5 digit as output. The output counts modulo-5 the number of times the pattern 358 has occurred in x(0, t). Give a state description of the system. Hint: Decompose the system into two: a pattern recognizer and a modulo-5 counter. The input set is I = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and the output set 0 = {0, 1, 2, 3, 4} . The state is formed of two components: s 1 to detect the pattern 358, and s 2 to count mod 5 the number of instances. For the pattern recognizer, we need three states as follows:
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Unformatted text preview: s 1 (t) = A if x(t - 1) = 3 s 1 (t) = B if x(t 2, t - 1) = 35 s 1 (t) = C if none of above s 1 (0) = C The state description of this component is The second component is a modulo 5 counter. Consequently, the state has five values which we label with the integers 0, 1, 2, 3 and 4 to be able to write the state transition as the arithmetic expression: Finally, the output function is z(t) = s 2 (t)....
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M16_2_Discussion6 - s 1 (t) = A if x(t - 1) = 3 s 1 (t) = B...

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