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Properties of code with summation for logical circuit test organization

Properties of code with summation for logical circuit test organization. A. Blyudov , D . Efanov , V . Sapozhnikov , Vl . Sapozhnikov. Petersburg State Transport University “Automation and Remote Control on Railways” department.

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Properties of code with summation for logical circuit test organization

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  1. Properties of code with summation for logical circuit test organization A. Blyudov,D.Efanov, V.Sapozhnikov, Vl.Sapozhnikov Petersburg State Transport University “Automation and Remote Control on Railways” department

  2. Properties of code with summation for logical circuit test organization, EWDTS`2012 2 Functional control system of the combinational circuit

  3. Properties of code with summation for logical circuit test organization, EWDTS`2012 3 Berger code S(n,m)-codes

  4. Properties of code with summation for logical circuit test organization, EWDTS`2012 4 Berger code The errors of an even multiplicity, which have the number of distortions of the informational bits of the type 10 equal to the distortions 01, cannot be detected in the S(n,m)-code. Formula for calculating the number of undetected errors d – multiplicity of undetectable error; m – length of informational word r – weight of informational word In S(8,5)-code 160 undetectable errors with d=2 & 60 undetectable errors with d=2

  5. Properties of code with summation for logical circuit test organization, EWDTS`2012 5 Berger code • In the S(n,m)-code the share of undetectable errors βddoesn’t depend on the number of informational bits and it is constant The Berger code has a great number of undetectable errors. Particularly, it doesn’t detect 50% of distortions of multiplicity 2

  6. Properties of code with summation for logical circuit test organization, EWDTS`2012 6 Modulo codes with summation Decreasing a number of check bits in the code with summation could be reached if the calculation of “ones” in the informational vector is carried out by some modulo M (M=2i<2k,i=1,2,…) SM(n,m)-codes • There are • modulo codes, besides the S(n,m)-code, • for any value of m.

  7. Properties of code with summation for logical circuit test organization, EWDTS`2012 7 Modulo codes with summation • All the errors of information bits of the odd multiplicity are detected in the modulo codes, but the errors of the even multiplicity may not be detected. • The share of the undetectable errors βd for a modulo code doesn’t depend on the number of informational bits and it is a constant value. • Any S2(n,m)-code (a parity code) doesn’t detect 100% of errors of informational bits of any even multiplicity. • Any S4(n,m)-code doesn’t detect 50% of errors of informational bits of any even multiplicity. • The SM(n,m)-code has the same number of errors of multiplicity d<M like the S(n,m)-code. • Any SM(n,m)-code with M≥4 doesn’t detect 50% of errors of informational bits of multiplicity 2. • The SM(n,m)-code with M≥8 has more errors of multiplicity d≥M than the S(n,m)-code. • The SM(n,m)-code has the value of characteristic βd equal or less than the same characteristic for the SM'(n,m)-code (M'>M) for every d. The properties of modulo codes

  8. Properties of code with summation for logical circuit test organization, EWDTS`2012 8 Modulo codes with summation Values of the characteristic βd

  9. Properties of code with summation for logical circuit test organization, EWDTS`2012 9 Modified modulo codes with summation The method of forming a RSM(n,m)-code is: 1. The S(n,m)-code is formed for the current m. 2. The modulo M is fixed:M=2,4,8,…,2b; b=]log2(m+1)[-2. 3. For the current informational word the number of “ones” q is counted, which is converted to the number W=q(modM). 4. The special coefficient α is determined. 5. If (), then α=0, otherwise α=1. 6. Then the resultant weight of an informational word is counted. 7. The check word is a binary notation of V. RSM(n,m)-codes

  10. Properties of code with summation for logical circuit test organization, EWDTS`2012 10 Classification of codes with summation

  11. Properties of code with summation for logical circuit test organization, EWDTS`2012 11 Classification of codes with summation The analysis tables for different codes allows to deduce the following conclusions: • 1. The RS(n,m)-codes have the best characteristics to detect errors. For example, the RS(21,16)-code has about by two times less undetectable errors in comparing with the Berger code, and this concerns to the errors of any multiplicity. • 2. Any modulo modified code with M≥4 has the better detection characteristics than any non-modified code. • 3. The modulo non-modified codes have an advantage in detecting errors among all the codes with the number of check bits d=2.

  12. Properties of code with summation for logical circuit test organization, EWDTS`2012 12 Conclusion The table of codes, in which the main characteristics of all the available codes with summation with a current number of informational bits are given, allows to choose a code more reasonably at organizing the check of a combinational circuit. Herewith there is a possibility to consider the properties of a control circuit, for example, the possibility of appearing errors of the determined multiplicity at the outputs of the circuit. A. Blyudov,D.Efanov, V.Sapozhnikov, Vl.Sapozhnikov Petersburg State Transport University “Automation and Remote Control on Railways” department

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