Concurrent ErrorDetection inALU's by Recomputing withShifted Operands
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A newmethod ofconcurrent error detection inthe Arithmetic andLogic Units (ALU's) isproposed. Thismethod, called "Recomputing with Shifted Operands" (RESO), candetect errors in boththearithmetic andlogic operations. RESOusestheprinciple of time redundancy indetecting theerrors andachieves its error detection capability through theuseofthealready existing replicated hardware intheformofidentical bitslices. Itisshownthat formostpractical ALU implementations, including thecarry-lookahead adders, the RESOtechnique will detect allerrors caused byfaults inabit-slice oraspecific subcircuit ofthebitslice. Thefault model usedismore general thanthecommonly assumed stuck-at fault model. Ourfault model assumes that thefaults areconfined toasmall areaofthecircuit andthat theprecise nature ofthefaults isnotknown. Thismodel is veryappropriate fortheVLSIcircuits. Furthermore, they arebased onthetraditional stuck-at fault modelwhichisnotappropriate fortheVLSItechnology. A moreappropriate assumption isthatthefailure inaVLSI circuit affects asmall areaofthechip andthenature ofthe failure isnotprecisely known. Forexample, imperfection in thesemiconductor material maybeconfined toasmall area ofthechip andthus affect several neighboring gates. Similarly, anincidence ofahighenergy particle mayalso affect asmall areaofthechip. Theunderlying failure mechanisms arenot well understood asyet. Therefore, itisunwise toassume that underfailure theoutput ofaspecific gateisstuck atsome logical value. Itistrue, however, that atsomehigher functional level theeffect offailures will befelt aschanges inlogical values. Thisfunctional level, forexample, canbeatthelevel ofabit-slice ofanALU.Thisisthelevel wechoose forour functional fault modelinthis paper. Throughout this paper, afailure inacircuit meanssomephysical malfunction; and anerror meansanincorrect value ofthefunction under con- sideration. Inthis paper wepresent anerror detection scheme based on timeredundancy. Inthenextsection, somesystematic ap- proaches ofdevising error detectionr bytimeredundancy are described. Later wedescribe theproposed error detection method, called Recomputing withShifted Operands (RESO). Theerror detection capabilities ofRESOaredescribed in Sections IVandV.Itisshownthat inatypical ALU,RESO detects allfunctional errors resulting fromfailures confined toacertain areaofthechip, forexample, abit-slice. InSection VIsomeextensions ofRESO,asrelated toerrror correction inlogic operations anderror detection inmultiply-divide circuits, arediscussed.
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