Download - Time Redundancy
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It Involves the Repetition or Rollback ofinstructions , Segment of programs or entire
programs immediately after a fault isdetected.
Rollback operation requires that a programrestarts processing from the last check point ,
where all the information relevant to thesuccessful execution of the program beyondthe check point is stored .
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The Selection of correct number of checkpoints is important .
If too many check points are used , the computation timeincreases since the normal flow of the program is stopped ateach check point in order to save state information.
The Recovery time will increase even if the check points are
too far apart since the program will have to be re-executedfrom the last check point .
The optimum check point interval is to be chosen to get theoptimum recovery time.
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If the fault is temporary , Rolling back the
program to a check point should allowsuccessful recovery .
If the fault is permanent , the fault detectionmechanism will be activated and analternative recovery method should beattempted.
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Distinguishing between Transient and
Permanent Faults
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The Key Advantage of Alternating Logic is that any
combinational circuit with n input variables can be transformed
into a self dual circuit with no more than n+1 variables
The dual of an n variable function f is given by
fd
= f_
( X1 ,_
X2 ,
_
, .. , Xn )
_
The function Fsd is Given by
fsd =
xn+1
f + xn+1 fd
_
Here Fsd is the
transformed
Self dual circuit of F
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Errordetection
mechanism
of ALU using
RESO
Technique
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The additional hardware required for thistechnique is the three shifters , the storageregister to hold the results of the first
computation and the comparator also. Also, the ALU must be extended by 2 bits to
allow a two bit , arthematic shift to beperformed.
Due to this extra bits required , we will go for
RESWO approach
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During the first computation, the operandsare manipulated in their standard form .
During the second computation , the upper
and lower halves of the operands are swappedsuch that a faulty bit slice operates on eitherthe lower or upper half of the operands duringthe first computation and the upper or lowerhalf of the operands during the secondcomputation .
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At t0,C1AC
C2Cout
At t0+
C1Cout
C2AC
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This method takes advantage of both Time
Redundancy and Hardware Redundancy.
In both RESO and RESWO methods error
detection is performed with the help of time
redundancy
But In this method,error detection accomplished
resembles that of duplication with comparision . Then Time redundancy is then used to complete
the calculation and obtain the final result
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For example, a 32 bit addition operation can
be realized by using each of two 16 bit adders
twice .
During each calculation, error detection is
accomplished by comparing the results from
using the two adders .
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32 bit
swapper
consists of32
2 -1 MUXs
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Time redundancy can provide error correction
if the computations are repeated for 3 ormore times.
Consider the logical and operation that was
illustrated in RESO method .
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OPERATION 1:
without shifting
OPERATION 2:
1BIT LEFT SHIFT
W.R.T ORIGINAL DATA
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OPERATION 3:
3BITS LEFT SHIFT
W.R.T. ORIGINAL DATA
By performing a majority vote on the 3 results
Error due to faulty bit slice can be corrected.
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Each of the three operations used operands
that were displaced from each other by atleast
one bit position , a different bit in each result
will be affected by the fault of bit slice .
The results due to faulty bit slice can corrected
by performing a majority vote on the three
results obtained for each bit position
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CONTRIBUTION
D.V.R.Reddy
Ramesh
Satesh
jitender
Gufran
Dubey
Jignesh
thakur
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References
P.k.lala
Barry W. Johnson