Controllability and observability notes for pg

Types of Measures
 SCOAP – Sandia Controllability and Observability Analysis Program
 Combinational measures:
 CC0 – Difficulty of setting circuit line to logic 0
 CC1 – Difficulty of setting circuit line to logic 1
 CO – Difficulty of observing a circuit line
 Sequential measures – analogous:
 SC0
 SC1
 SO

Range of SCOAP Measures
 Controllabilities – 1 (easiest)
 Observabilities – 0 (easiest)
 Combinational measures:
– Roughly proportional to # circuit lines that must be set
to control or observe given line
 Sequential measures:
– Roughly proportional to # times a flip-flop must be
clocked to control or observe given line

Goldstein’s SCOAP Measures
 AND gate O/P 0 controllability:
output_controllability = min (input_controllabilities)
+ 1
 AND gate O/P 1 controllability:
output_controllability = S (input_controllabilities)
+ 1
 XOR gate O/P controllability
output_controllability = min (controllabilities of
each input set) + 1
 Fanout Stem observability:
S or min (some or all fanout branch observabilities)

Observability Examples
To observe a gate input:
Observe output and make other input values non-controlling

More Observability Examples
To observe a fanout stem:
Observe it through branch with best observability

Controllability Through Level 0
Circled numbers give level number. (CC0, CC1)

Controllability Through Level 2

Final Combinational Controllability

Combinational Observability for Level 1
Number in square box is level from primary outputs (POs).
(CC0, CC1) CO

Combinational Observabilities for
Level 2

Controllability and observability notes for pg

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