Теория управления / Л4-Миль-Мур-СА / pics / 6-sequential logic-31
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example
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A.J. Han Vinck |
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Step 1:
Group together states with same outputs
(1,3,6,8) (2,5) (4,7)
Step 2: further subdivide groups into subgroups with same transition
(1,3,6,8) (2,5) (4) (7)
STOP:
4 Representants: 1, 2, 4, 7
41
Example: reduced table
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A.J. Han Vinck |
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Another example
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input = 0 |
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input = 1 |
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Step 1: Group together: same output
[ A B C E F G] [D]
Step 2: group according to transition
[A,B,E,F,G] [C] [D]
Step 2: group according to transition
[A,B] [E,F,G] [C] [D]
Step 2: group according to transition [A,B] [E,F,G] [C] [D]
no change: END
DEF: two states are equivalent if and only if, for any input of length k, k > 0, they give rise to the same output.
A.J. Han Vinck |
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A famous computer scientist
http://www-cs-faculty.stanford.edu/~knuth/
Donald E. Knuth
Professor Emeritus of The Art of Computer Programming at Stanford University
The Art of Computer Programming (TAOCP)
Famous quote: Beware of bugs in the above code; I have only proved it correct, not tried it.
A.J. Han Vinck |
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example
•Check for sub-string 100 in a binary sequence
Example: input |
00101000100000 |
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output |
00001000100000 |
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Binary input sequence |
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–Output = 1 if 100 detected |
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–Output = 0 otherwise |
clock
•Every time unit, the system
–Output = 1 if true
–Output = 0 otherwise
A.J. Han Vinck |
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example
Keep 2 bits in memory and look for the next input:
Example: input |
00101000100000 |
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output |
00001000100000 |
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State table
Old state ( xt-1 xt-2) |
new state(xt xt-1 ) |
output |
= xt xt-1‘ xt-2‘ |
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input xt |
input xt |
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10 equivalent to 11
A.J. Han Vinck |
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Example implementation
input xt
xt-1
xt-2
Output = xt xt-1‘ xt-2‘
Homework:
Consider the table with reduced number of state
What are the consequences for the implementation?
Draw the Markov state diagram(also in the reduced form)
A.J. Han Vinck |
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Example, state diagram
State: last 2 incoming bits
Output: 0 or 1
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Reduced state diagram |
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Output: 0 or 1 |
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10/11 |
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Q: how many 1‘s do you |
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expect in the output? |
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Q: does it depend on the |
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probability of 1 and 0 in |
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the input sequence? |
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A.J. Han Vinck |
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We end with shift registers and counters
1.basic registers (serial-parallel)
2.some applications
3.counters
A.J. Han Vinck |
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A basic register
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A.J. Han Vinck |
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