LOGIC14_r2 - Chapter 14 Derivation of State Graphs &...

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Chapter 14 Derivation of State Graphs & Tables
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The detector will examine a string of 0’s & 1’s applied to the X input and generate an output Z=1 only when a prescribed input sequence occurs. In this network, any input sequence ending in 101 will produce an output Z=1 coincident with the last 1. i.e., Z=1 iff X=101. § Sequence Detector
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A typical input and corresponding output X= 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 0 Z= 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 time: 0 1 2 3 4 5 6 7 8 9 101112131415
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Mealy network: X/Z 1. Start the network in a reset state designated S 0 . 2. If a “0” input is received, the network can stay in S 0 since the input sequence we are looking for does not start with “0”. 3. If a “1” is received. We must go to a new state S 1 to remember that the first input in the desired sequence has been received.
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4.When in state S 1 , if we receive a “0”, the network must change to a new state S 2 to remember that the first two inputs of the desired sequence (10) have been received. If a “1” is received in S 2 , the desired input sequence (101) is complete and the output should be 1. When in state S 1 , if a “1” is received, we can stay in S 1 since the sequence is simply restarted. 5.If a “0” occurs in state S 2 , two “0”s are received and we must reset the network to state S 0 .
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So, the state graph for sequence detector.
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State Table Present Next State Present Output State X=0 X=1 X=0 X=1 S 0 S 0 S 1 0 0 S 1 S 2 S 1 0 0 S 2 S 0 S 1 0 1
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Since one FF can have only two states, two FFs are needed to represent the three states. Designate the two FFs as A&B. Let A=0, B=0, state S 0 A=0, B=1, state S 1 A=1, B=0, state S 2 therefore, A + B + Z A B X=0 X=1 X=0 X=1 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 0 1
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The next-state maps
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LOGIC14_r2 - Chapter 14 Derivation of State Graphs &...

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