Integral Humanism
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Transcript Integral Humanism
Gheorghe M. Ştefan
http://arh.pub.ro/gstefan/
- 2014 -
Veitch-Karnaugh diagrams
m0 = a’b’c’d’
m1 = a’b’c’d
m2 = a’b’cd’
m3 = a’b’cd
m4 = a’bc’d’
m5 = a’bc’d
m6 = a’bcd’
m7 = a’bcd
m8 = ab’c’d’
m9 = ab’c’d
...
m15 = abcd
Are based on the minimal Hamming distance
between adjacent cells
Veitch version
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Karnaugh version
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Minimizing logic functions
smallest number, of rectangular
surfaces of 1’s, with maximal area,
containing 2i 1’s, and including all 1’s
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“don’t care”s
a’b +a’c
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b+c
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V-K’s with included functions
Is a two-step process:
1. Only 1’s
2. 1’s become “don’t’ care”s
(bc’d + a’bc’ + b’c) + (acde + c’de’)
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Transition diagrams
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Moore version
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Mealy version
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Verilog modules
Immediate Moore version for ‘bb detector’
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State transition function:
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Output transition function:
For the delayed version:
always @(posedge clock)
case(state)
init_state : out <= no;
. . .
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For the immediate Mealy version of ‘bb
detector’ only the output function is
different:
For the delayed version the change is similar as for Moore
version
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Automata are complex circuits
The number of lines in the Verilog description:
Are equal with the number of states for the behavioral
descriptions
Are equal with the number of gates used for the structural
descriptions
The transition diagrams have the size in
O(|Q| log |Q|)
Because they are complex we must keep them small
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State coding
First coding
Second coding
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First version:
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Second version:
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Coding styles
Minimal variation encoding:
successive states are coded with minimal Hamming
distance
Reduced dependency encoding:
minimal Hamming distance for states preceded by
the same state
Incremental encoding:
whenever possible successive state are coded by
incremented values
One-hot state encoding:
one bit per state
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Minimal variation encoding
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Reduced dependency encoding
Reduced dependency on both, X0 and X1 has no solution
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Parasitic effects in automata
Automata with asynchronous inputs
Automata with asynchronous outputs
Hazard generated by asynchronous inputs
Propagation hazard
Dynamic hazard
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Automata with
asynchronous inputs
If the input variable switches asynchronously the input
of the state register can vary in the prohibited time –
tsu + t+ +th
No problems if only one bit switches:
00 -> 01 => 00 -> 01 or 00 -> 00
Big problems if more than one bit switch:
01 -> 10 => 01 -> 10 or 01 -> 00 or 01 -> 11 or 01 -> 01
The automaton evolves wrongly in the state space
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The solution:
reduced dependency state coding
What can be done if there are state transitions depending
on two or more asynchronous input variable ?
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Asynchronous outputs:
hazard due to asynchronous inputs
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Asynchronous outputs:
propagation hazard
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Avoiding propagation hazard
Partial protection
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Full protection
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Dynamic hazard
Due to many-level combinational circuits (ex: carry
propagation)
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Fundamental limits
The asynchronous input bits can be considered only
independently in distinct states
Immediate Mealy automata with asynchronous inputs
can not have actual implementations (unpredictable
outputs)
Delayed Mealy automata with asynchronous inputs
can not have actual implementations (the state and
outputs could evolve uncorrelated)
Hazard free Moore with asynchronous inputs have no
actual solution (state must be encoded simultaneously
with minimal variation and reduced dependency)
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Home work 9
Problem 1:
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