Self checking circuits delay insensitive codes and self checking checkers
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Self-Checking Circuits Delay-Insensitive Codes and Self-Checking Checkers. Self-Checking Circuits. Most important factors in designing a digital system: Speed, Cost and Correctness. Some systems used in 1. medical equipment used in ICUs, 2. aircraft control systems,

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Self-Checking Circuits Delay-Insensitive Codes and Self-Checking Checkers

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Self checking circuits delay insensitive codes and self checking checkers

Self-Checking Circuits Delay-Insensitive CodesandSelf-Checking Checkers


Self checking circuits

Self-Checking Circuits

  • Most important factors in designing a digital system:

  • Speed, Cost and Correctness.

  • Some systems used in

    • 1. medical equipment used in ICUs,

    • 2. aircraft control systems,

    • 3. nuclear reactor control systems,

    • 4. military systems and

    • 5. computing systems used in space missions.

  • High reliability is of the utmost importance.

  • DSM technology: Signal Integrity problem


Self checking circuits1

Self-Checking Circuits

  • Def: Self-Checking Circuit

    • Circuits detecting faults in normal operation.

  • Testing vs self-checking?

  • Faults: stuck at zero and stuck at one

    • stuck at one in one input of an 2-input OR gate?

    • stuck at zero in one input of an 2-input OR gate?

    • stuck at one in one input of an 2-input AND gate?

    • stuck at zero in one input of an 2-input AND gate?


Self checking circuits2

Self-Checking Circuits:

  • Def: Error

    • An incorrect output caused by a stuck-at fault.

  • Def: Single Error

    • An error that affects only a single component value

  • Def: Multiple Error

    • An error that affects multiple component values.

  • The component value affected by an error may

  • change form 0 to 1, or vice versa.

  • Def: unidirectional errors

  • When all components affected by a multiple error

  • change their values monotonically.


Self checking circuits3

Self-Checking Circuits:

  • Def: Error Detecting Code

  • Def: Hamming distance of two vectors x and y

  • the number of components in which they differ.

  • Def: Hamming distance of a code X

  • the minimum of the Hamming distances between all

  • possible pairs of code words in X.


Self checking circuits4

Self-Checking Circuits:

  • Lemma: A code with Hamming distance d+1

  • can detect all errors with weight d or less.

  • Lemma: A code with Hamming distance 2c+1

  • can correct all errors with weight c or less.

  • One-Hot Code:

  • 1. Delay-Insensitive Code

  • 2. Detect one error (H.D.=2).


Fault tolerant systems masking scheme

Fault-tolerant Systems:masking scheme:

  • 1. All of the redundant modules are active at all times.

  • 2. When a fault occurs, the faulty module is masked.

  • 3. The most common masking scheme is

  • triple modular redundancy in which the outputs

  • of three copies of function units are fed to a

  • majority gate.

  • 4. If one of the three modules becomes faulty,

  • the two remaining fault-free modules mask the

  • results of the faulty one when the majority vote

  • is performed.


Fault tolerant systems standby scheme

Fault-tolerant Systems:Standby scheme:

  • 1. only one copy of the system is active.

  • 2. When the active module detects the occurrence

  • of faults, the standby module is activated and

  • takes over the control.

  • 3. Thus, to use self-checking circuits in a

  • fault-tolerant system, double module redundancy

  • is sufficient.

  • 4. This scheme may be superior than the former

  • in terms of power consumption and hardware cost.


Self checking scheme

Self-checking scheme

  • Self-Checking scheme:

    • 1. a self-checking functional unit.

    • 2. a self-checking checker.

Self-Checking

functional unit

Inputs

X

Outputs

Y

...

...

...

...

Self-checking

checker

X: input code space

Y: output code space

Error signal


Self checking circuits5

Self-Checking Circuits

  • During the fault-free operation:

  • a normal input will produce a normal output.

  • If an incorrect output is produced due to a fault,

  • the error should be detected by the self-checking

  • checker.


Self checking scheme1

Self-checking scheme


Self checking scheme2

Self-checking scheme

  • Fault Secure(FS):

  • code word input to a faulty circuit must not

  • produce an incorrect code word output.

  • Self-testing:

  • a fault in a circuit must be detected by some

  • input.


Self checking scheme3

Self-checking scheme

  • Fault Secure(FS):

  • Self-testing:


Self checking scheme4

Self-checking scheme

  • Totally Self-Checking:

  • Partially Self-Checking:


Self checking scheme5

Self-checking scheme

  • Fault-secure-only circuits:

    • 1. No erroneous results go undetected.

    • 2. However, it is possible that some fault can

    • never be detected.

  • Self-testing-only circuit:

    • 1. Any fault can produce undetected errors for a

    • short time.

    • 2. However, there is a code word input that can

    • detect the fault.


Self checking scheme6

Self-checking scheme

  • Totally self-checking circuit:

    • 1. no erroneous results go undetected and

    • 2. any fault will be eventually detected.

  • Partially self-checking circuits:

    • 1. This approach is to restrict the set of faults for

    • which the circuit has to be checked.

    • 2. They are introduced to provide low-cost error

    • detection.

    • 3. They may be used in non-critical applications.


Self checking circuits delay insensitive codes and self checking checkers

Delay-Insensitive Tree Adder


Self checking checkers

Self-Checking Checkers

  • Code-disjoint:

  • TSC Checker:

With the code-disjoint feature, one may be able to

test if the TSC checker is malfunction.


Di adder checker

DI Adder Checker

  • Code word input: one-hot code of output signals

    • (adder)

  • Correct code word output Z0 Z1 = 10

  • Incorrect code word outputs Z0 Z1 = {00 01 11}


  • Delay insensitive codes

    Delay-Insensitive Codes

    • M/N code (M<N): M-out-of-N code

    • all valid code words have exactly M 1’s and N-M O’s.

    • Length of M/N code: C(N,M)

      • 1. One-hot code(1/N code):

      • a. dual-rail encoding: (01 10)

      • b. 1/3 code: (001 010 100)

      • c. length of one-hot code: C(N,1)

      • 2. Optimal M/N code: M=N/2

      • a. 3/6 code: (000111,001011,001101,001110, …)

      • b. length of M/N Code = C(N, N/2)

    • Berger Code, Modified Berger code:


    Delay insensitive transmission

    Delay-Insensitive Transmission

    Sender

    Receiver

    I

    I

    DI codes

    decoder

    encoder


    Delay insensitive transmission1

    Delay-Insensitive Transmission

    • Cost factors:

    • Number of Wires (cost)

    • Encoder (logic complexity/computation time)

    • Decoder (logic complexity/computation time)


    Delay insensitive codes berger

    Delay-Insensitive Codes: Berger

    • Berger Code:

      • 1. Systematic code: Information bits + Check bits

      • (note that M/N code is a nonsystematic code).

      • 2.

      • 3. Check bits = counting the number of 0’s in I bits.

      • 4. See table (Next page)


    Delay insensitive codes1

    Delay-Insensitive Codes


    Delay insensitive transmission berger codes

    Delay-Insensitive Transmission: Berger codes

    DI codes

    Sender

    Receiver

    I’

    Check

    bits

    I

    C’’

    C

    C’

    Check

    bits

    Compare

    Valid?


    Self checking checkers1

    Self-Checking Checkers:

    • Self-checking Checkers of M/N code

      • 1. One-hot code(1/N code):

      • a. dual-rail encoding: (01 10):

      • shown in DI Adders

      • b. 1/N code:

      • c. Z0: completion signal

      • Z1: error detection

    C(N,2)

    ...

    &

    &

    &

    ...

    +

    +

    Z1

    Z0


    Self checking checkers2

    Self-Checking Checkers:

    • Self-checking Checkers of M/N code

      • 2. Optimal M/N code: M=N/2

      • a. 3/6 code: (000111,001011,001101,001110, …)

      • b. length of M/N Code = C(N, N/2)

    C(N,N/2)

    N/2+1

    C(N,n/2+1)

    N/2

    ..

    ..

    ...

    ...

    &

    &

    &

    &

    &

    &

    +

    +

    Z0

    Z1


    Self checking checkers3

    Self-Checking Checkers:

    • Use Sorting Networks for Self-checking Checkers:

    • General sorting network:

    A1

    An

    Sorting

    Network

    Max(A1, … , An)

    Min(A1, … , An)

    n

    unsorted

    numbers

    n

    sorted

    numbers

    ...

    ...

    A1

    A2

    Max(A1,A2)

    Min(A1, A2)

    Comparator


    Self checking checkers4

    Self-Checking Checkers:

    • Binary sorting network:

    x1

    xn

    Sorting

    Network

    1 k 1’s

    1

    0 n-k o’s

    0

    n

    binary

    input

    ...

    ...

    ...

    x1

    x2

    Max(x1,x2)= x1+x2

    Min(x1, x2)= x1x2

    Comparator


    Self checking checkers5

    Self-Checking Checkers:

    • Binary sorting network for 2/4 code

    CMP

    CMP

    CMP

    CMP

    CMP


    Error collection codes

    Error Collection Codes:

    • Code with HD>=3 may correct error

    • Ex. HD=4: 0011 1100


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