# Patent

## Title
Electronic circuit arrangement for processing binary input values

## Abstract

Electronic circuit arrangement for processing binary input values xεX of a word width n (n>1), with a first, second and third combinatory circuit components configured to process the binary input values x to form first, second and third binary output values. The arrangement further includes a majority voter element configured to receive the binary output values and provide a majority signal based on the received binary output values. The second and third combinatory circuit components are designed, as regards faults during processing of the binary input values x in the first combinatory circuit component, to process binary input values of a true non-empty partial quantity X1 of the quantity of binary input values X in a fault-tolerant manner and process binary input values of a further non-empty partial quantity X2 of the quantity of binary input values X different from the true non-empty partial quantity X1 in a fault-intolerant manner.

## Background
The disclosure relates to the field of error correction in an electronic circuit.
BACKGROUND
The level of integration of electronic circuits has been increasing for many years. The dimensions of circuit elements such as transistors, the dimensions of connecting structures, current intensity and voltage values are forever getting smaller. As a result of this there has been a rise in error frequency.
It is known to make circuits or parts of a circuit fault-tolerant in respect of a multitude of faults by tripling the circuits. A circuit S is tripled to give three circuits S1, S2 and S3, which are functionally equal to circuit S. The outputs of circuits S1, S2 and S3 are connected to a voter V which performs a majority decision. System triplication also called TMR has been described, for example, in Barry W. Johnson “Designs and Analysis of Fault Tolerant Digital Systems”, Addison Wesley Publ. Comp. Reading, Mass., 1989, p. 51-53 and U.S. Pat. No. 6,963,217 B2. A random fault in one of the three partial systems S1, S2 and S3, which for any given input value affects the output of one of circuits S1, S2 or S3, is tolerated by a TMR system.
In practical applications it is sometimes merely necessary for the fault-tolerant system to behave especially reliably only for the input of certain defined values, whilst for other input values no such high reliability of output values is required. For example, a circuit for triggering an airbag in cars should produce the control signals for tripping the airbag with an especially high degree of reliability when inputting the corresponding tripping signal, whilst production of the control signals for opening and closing the central locking system is not subject to such a high reliability requirement.
The disadvantage with the known triplication of a system with voter is the fact that it requires a great deal of hardware, that energy consumption is more than three times as high in comparison to the original system and in that it is not possible to vary the reliability for different input values which from the start require different reliability levels.
SUMMARY
It is an object to propose an improved electronic circuit arrangement comprising a plurality of combinational circuit arrangements for processing binary input values in a fault-tolerant manner, which is realizable but costs less to produce.
An electronic circuit arrangement or device for processing binary input values according to independent claim 1 is provided. Advantageous embodiments are the subject of dependent sub-claims.
Due to the fault-tolerance for input values from a non-empty subset X1 of all input values X and no fault tolerance for input values from a further non-empty subset X2 of all input values X the expenditure for realising the circuit arrangement with respect of the known system triplication and the majority decision can be reduced. It is advantageous if the subset X1 of the input values for which the circuit arrangement is to be fault-tolerant can be fixed in such a way that all necessary requirements as regards the fault tolerance of the circuit arrangement are met. Expenditure on hardware is less since the cost for implementation can be adapted to suit the necessary fault-tolerance.
A further development provides for the second and third combinational circuit components to be further designed to incorporate the following features:

    
    
        in a fault-free case the second binary output value of the second combinational circuit component and the third binary output value of the third combinational circuit component are equal to the first binary output value of the first combinational circuit component, for all binary input values of the non-empty proper subset X1,
        for all binary input values from the further non-empty subset X2 the second binary output value of the second combinational circuit component and the third binary output value of the third combinational circuit component are non-equal, and
        for all binary input values of the subset X1 the following is true
        for each bit of the first combinational binary output value of word width a1: at least the second binary output value of the second combinational circuit arrangement or at least the third binary output value of the third combinational circuit component is equal to the first binary output value of the first combinational circuit component.
    
    


With an advantageous design provision may be made for the second combinational circuit component to be configured so as to process the binary input values x such that the second binary output value is equal to the first binary output value.
One embodiment provides for further combinational circuit components each of which are configured to process the binary input values x to form the first binary output value, and the output of which is respectively connected to an input of the majority voter element. If, for example, two further circuit components are present which process binary input values to form the first binary output values, the fault tolerance for input values from the partial quantity X1 is equal to the fault tolerance of a quintupled system with majority decision without requiring hardware expenditure for a quintupled system with majority decision.
A further development of the invention can provide further majority voter elements whose input for receiving the respective binary output value is connected with the output of all combinational circuit components and which are respectively configured, depending upon the received binary output values, to provide a majority signal at their output. In one design exactly two further majority voter elements are formed. This design enables faults to be tolerated also in a voter element.
With respect to a preferred embodiment, the respective input of all combinational circuit components is serial-connected with an output of a further circuit component, wherein the further circuit component is configured to process binary input values uεU to form binary output values W which, at least partially, are different from the binary input values xεX, wherein X1⊂W. If certain input values of the combinational circuit components are produced with the aid of the serial connected further circuit not as output values, the circuit arrangement provided can realise the fault tolerance only for the actually present input values or for a subset of these input values. The values not occurring as output values of the further circuit provided need not be added to the quantity X1, for which a fault tolerance is required, resulting in a reduction in expenditure for a realisation without the fault tolerance being diminished.
With an advantageous design provision is made for a further combinational circuit component configured to process the binary input values x to form binary control signals and a multiplexer element, wherein

    
    
        the output of the further combinational circuit component carrying the binary control signals is connected with the control input of the multiplexer element,
        a first data input of the multiplexer element is connected with the output of the first combinational circuit component, and
        a second data input of the multiplexer element is connected with the output of the majority voter element.

In this design individual faults of the circuit component are tolerated especially advantageously.

    
    


A convenient further development may provide for the binary input values of non-empty subset X1 to form a subset of binary input values, so that for a set Φ of faults φ1, . . . , φk occurring in the first circuit component the following is true: S(x)≠S(φ,x) for xεX1, wherein S(φ, x) is the binary output value of the first combinational circuit component, if fault φεΦ is present and the binary input value x is input. In this way the system can be secured against certain faults in critical areas.
One embodiment provides for X2=(X\X1).
In an advantageous design provision is made for the binary output value of the second circuit component to be 1 and for the binary output value of the third combinational circuit component to be 0 for the binary input values from the further non-empty subset X2.



DESCRIPTION OF PREFERRED EMBODIMENTS
Embodiments will now be explained in more detail with reference to figures of the drawing, in which:
FIG. 1 is a schematic illustration of a known combinational circuit,
FIG. 2 is a schematic illustration of a known combinational circuit with triplification,
FIG. 3 is a schematic illustration of a combinational circuit according to one embodiment,
FIG. 4 is a schematic illustration of a combinational circuit according to the embodiment of FIG. 3 with a typical circuit implementation,
FIG. 5 is a schematic illustration of a combinational circuit according to a further embodiment,
FIG. 6 is a schematic illustration of a combinational circuit according to an embodiment with an additional circuit for generating a control signal and with a multiplexer element,
FIG. 7 is a schematic illustration of a combinational circuit according to an embodiment with further combinational circuit components,
FIG. 8 is a schematic illustration of a combinational circuit according to an embodiment with several voter elements,
FIG. 9 is a schematic illustration of a combinational circuit according to an embodiment with an upstream circuit element, and
FIG. 10 is a schematic illustration of a further combinational circuit.



FIG. 1 shows a known combinational circuit S 11, which for an input value x from an input set X outputs a value y=S(x), so that the circuit S 11 realises the function S(x). The word width of the input of S 11 is m and the word width of the output is n. Therein: m>1 and n≧1.
FIG. 2 shows, how according to the state of the art a fault-tolerant so-called TMR (Triple Modular Redundancy) system can be realised from S 11 with m>1 and n≧1 through system triplication and a voter.
The combinational circuit S 11 of FIG. 1 has been triplicated to form 3 combinational circuits S121, S222, S323. The three circuits S121, S222 and S323 realise the functions y1=S1(x), y2=S2(x) and y3=S3(x), which respectively equal the function y=S(x). Therefore it is true for all xεX that S1(x)=S2(x)=S3(x)=S(x). The output with a width of n-bit of circuits S121, S222 and S323 are connected to three n-bit wide inputs of a voter V 24, which at its output outputs the n-bit wide signal y. For each bit of its n-bit wide inputs the voter outputs the value which occurs most frequently. If y1=(y11, . . . , y1n), y2=(y21, . . . , y2n), y3=(y31, . . . , y3n), y=(y1, . . . , yn), then for i=1, . . . , n the value of yi is determined as yi=(y1iy2i)(y1iy3i)(y2iy3i). Voters with 3 or more inputs are known to the expert.
FIG. 3 shows a combinational circuit with a set X of possible input values, which is fault-tolerant for a true or proper subset X1⊂X of its input values and whose realisation expenditure is less than a TMR realisation. In contrast to a TMR realisation according to the state of the art such as described in FIG. 2, where the combinational circuit S 11 has been replaced by three functionally equal circuits S121, S222, S323, the combinational circuit S 11 of FIG. 1 in the circuit according to the invention of FIG. 3 has been replaced by three circuits S131, s232 and s333, which are not all functionally identical. The circuits S131, s232 and s333 are also called the first, second and third combinational circuit component of the circuit arrangement according to the invention of FIG. 3. In there A1 with A1=n is the number of binary outputs of the first circuit component and a1 is the number of binary outputs of the second and third circuit component, wherein a1≦A1. In order to illustrate the principle of the invention as clearly as possible, it is assumed for FIG. 3 that both S131 and s232 as well as s333 have only one binary output, so that the output word width a1 is equal to 1. Circuit S131 realises the same function y=S1(x)=S(x) as circuit S 11. Circuits s232 and s333 realise the functions y2=s2(x) and y3=s3(x), wherein for xεX1: s2(x)=s3(x)=S1(x).
Thus: if the input value x is from the first subset X1 of X, then S131, s232 and s333, in the fault-free case, output the same values respectively. For xε(X\X1) at least one of values s2(x) or s3(x) output by s232 or s333 is equal to S1(x), which is formally expressed by (s2(x)=S1(x))(s3(x)=S1(x)) for xε(X\X1). There is a non-empty subset X2⊂(X\X1) of X\X1 for which s2(x)≠s3(x) for xεX2, and for xεX2 only two and not all three of values S1(x), s2(x) and s3(x) are equal. Thus for the input values x with xεX1, as already mentioned: S1(x)=s2(x)=s3(x).
For xεX1 the circuit arrangement of FIG. 3 has the same fault tolerance characteristics as the circuit arrangement of FIG. 2, whilst the circuit arrangement of FIG. 3 for xεX2 is not fault-tolerant. Due to the fact that fault tolerance is required only for certain input values and not for all xεX, the fault tolerance characteristics can be accurately adapted and circuit expenditure for the circuit arrangement in FIG. 3 is often surprisingly considerably reduced compared to the circuit expenditure in FIG. 2, which is advantageous.
In table 1 the truth table of a Boolean function S1(x)=S1(x1, x2, x3) is shown, which shall be realised by a fault-tolerant circuit arrangement according to FIG. 3. y=S1(x), x1, x2 and x3 are binary variables.











TABLE 1





x1
x2
x3
S1(x)
X1







0
0
0
0
+


0
0
1
1
+


0
1
0
0


0
1
1
1
+


1
0
0
1


1
0
1
0


1
1
0
1


1
1
1
1









The set of all possible input values of the circuit is X={000,001,010,011,100,101,110,111}. The subset of input values X1, for which circuit S is fault-tolerant, is X1={000,001,011}. A possible representation of the Boolean function S1(x) is for example

S1(x)=(x1⊕x3)(x1x2x3)  (1.1)

wherein ⊕ stands for the XOR or anti-valence operation,  for the OR operation (disjunction) and  for the AND operation (conjunction). Equation (1.1) is checked most simply by inserting all 8 values for (x1x2x3)εX. The input values 000, 001 and 011, which belong to X1, are marked in table 1 with + in the column headed X1. In table 2, in addition to the values of function S1(x) of table 1, the values of functions s2(x) and s3(x) have been entered, which are realised by circuits s2 and s3.
















TABLE 2





x1
x2
x3
S1 (x)
X1
s2 (x)
s3 (x)
X\X1
X2







0
0
0
0
+
0
0




0
0
1
1
+
1
1


0
1
0
0

0
1
+
+


0
1
1
1
+
1
1


1
0
0
1

0
1
+
+


1
0
1
0

0
1
+
+


1
1
0
1

0
1
+
+


1
1
1
1

0
1
+
+









The input values belonging to the subsets X\X1 and X2, respectively, are marked by an + in the columns headed X\X1 and X2 respectively. Table 2 shows that the subsets X\X1 and X2 are the same. Possible representations of the Boolean functions s2(x) and s3(x) are

s2(x)= x1x3  (1.2)

s3(x)=x1x2x3  (1.3)

FIG. 4 shows an embodiment of the circuit arrangement according to FIG. 3 with circuits S=S1, s2 and s3, which realise the functions S1(x), s2(x) and s3(x) described by table 2 and by equations (1.1), (1.2) and (1.3).
The circuit arrangement of FIG. 4 consists of circuits S141, s242, s343 and a voter V 49. Circuit S1 consists of XOR gate 44, AND gate 45 and OR gate 46. Circuit s242 consists of AND gate 47 and circuit s343 consists of OR gate 48. The input line carrying input signal x1 is connected with the first input of XOR gate 44, the first input of AND gate 45, the first input of OR gate 48 and in a negated manner with the first input of AND gate 47. The input line carrying input signal x2 is connected with the second input of AND gate 45 and with the second input of OR gate 48. The input line carrying input signal x3 is connected with the second input of XOR gate 44, the third input of AND gate 45, the second input of AND gate 47 and the third input of OR gate 48. The output of XOR gate 44 is connected with the first input of OR gate 46, the second input of which is connected with the output of AND gate 45 and whose output carrying the signal y1 is fed into the first input of voter V 49. The output of AND gate 47 carrying the value y2 is connected with the second input of voter V 49. The output OR gate 48 carrying the signal y3 is fed into the third input of voter V 49. Voter V 49 outputs the signal y at its output.
The circuit S141 comprises 3 gates: XOR 44, AND 45 and OR 46, whilst circuit s242 comprises only AND gate 47 and circuit s343 comprises only OR gate 48. It is clear that circuits s2 and s3 require less expenditure for their realisation than S1. If for example input value (x1, x2, x3)=001 from the subset X1 is input, gates 46, 47 and 48, in a fault-free case, respectively output the value y1=y2=y3=1, which voter V 49 uses for performing the majority decision y=1.
Let it be assumed that a stuck-at-0 fault is present at the first input of OR gate 46, which is connected with the output of XOR gate 44. The value at this input then is constantly 0, and for an input of 001 from X1 the OR gate 46 and thus the circuit S141 outputs the erroneous value 0. Since circuits s242 and s343 are not affected by this fault, they continue to output the value 1 so that voter V 49 forms the correct output value y=1 from its input value (y1y2y3)=011, whereby the error due to this fault is tolerated.
Similarly errors or faults in the partial circuits s2 or s3 are tolerated when inputting values xεX1. A fault at the output of circuit s242 may thus be caused in that at the second input of AND gate 47, which carries the signal x3, a stuck-at-0 fault occurs resulting in this input always carrying the value 0. When inputting 001 the output of AND gate 47 then shows the value 0 instead of the correct value 1 and circuit s242 outputs the faulty value 0. Circuits S141 and s343, however, output the respectively correct value of 1, resulting in the voter V 49 generating the correct result y=1.
For the same fault, given an input of 011, a value of 1 is present at the output of XOR gate 44 and a value of 0 is present at the output of AND gate 45, so that the OR gate 46 and thus the circuit S141 outputs a value of 1. The output of OR gate 48 and thus the output of circuit s343 also show a value of 1. The output of AND gate 47 and thus the output of circuit s242 shows a value of 0. The voter V 49 forms the majority signal 1 from the signals 101 present at its inputs, and the error or fault of circuit s242 is tolerated for an input of 011 from the subset X1. Thus the general result is that each error due to a fault affecting only one of partial circuits S1, s2 or s3 is tolerated for an input of an arbitrary xεX1 by the circuit according to FIG. 4.
In a further embodiment a combinational circuit S with 3 inputs x1, x2, x3 and A1=3 binary outputs y1, y2, y3 shall now be considered. The combinational circuit S realises the three Boolean functions S11(x)=y1, S12(x)=y2, S13(x)=y3 the table of values of which are shown in table 3. Thus x=(x1,x2,x3), and the three Boolean functions S11(x), S12(x), S13(x) are combined to form S1(x)=(S11(x), S12(x),S13(x)). The first output of circuit S, which implements function S11(x), is supplemented by two further outputs of additional circuits s21 and s31, which implement the Boolean functions s21(x) und s31(x). The second output of circuit S, which implements the function S12(x), is supplemented by two further outputs of additional circuits s22 und s32, which implement the Boolean functions s22(x) and s32(x). The third output of circuit S, which implements the function S13(x), is not supplemented by further outputs, since no fault tolerance is required for this circuit output. The first circuit component thus realises the Boolean functions S11(x), S12(x) and S13(x) at their A1=3 binary outputs. The second circuit component realizes the Boolean functions s21(x) und s22(x) at their a1=2 binary outputs, whilst the third circuit component realizes the Boolean functions s31(x) and s32(x) at their a1=2 binary outputs. The fault tolerance here is realised only for the output values of word width a1=2, which are output at the first two binary outputs of all A1=3 circuit outputs of circuit component S1. The second and third circuit components s2 and s3 therefore comprise only a1=2 binary circuit outputs, respectively.
For X1={011}, i.e. for the input value 011, a circuit arrangement according to the invention is to be determined, which is fault-tolerant for the first two outputs y1 und y2. No fault-tolerance is provided for input values X\X1={000,001,010,100,101,110,111}. Independently of any input no fault-tolerance may be required for output y3.













TABLE 3





x1
x2
x3
S11 (x) = y1
S12 (x) = y2
S13 (x) = y3
X1







0
0
0
0
1
0



0
0
1
0
0
1


0
1
0
1
1
1


0
1
1
0
1
0
+


1
0
0
1
0
0


1
0
1
0
0
1


1
1
0
0
0
1


1
1
1
1
1
0









Table 4 shows a truth table for the functions S11(x), S12(x), S13(x), s21(x), s22(x), s31(x), s32(x), which meets the fault-tolerance requirements for input value 011. Table 4 reveals that the following applies to x=(011)εX1={011}:

S11(011)=s21(011)=s31(011)=0

S12(011)=s22(011)=s32(011)=1.

In other respects the following applies to all xε(X\X1),

[S11(x)=s21(x)] or [S11(x)=s31(x)]

and

[S12(x)=s22(x)] or [S12(x)=s32(x)].


















TABLE 4





x1
x2
x3
S11 (x)
S12 (x)
S13 (x)
s21 (x)
s22 (x)
s31 (x)
s32 (x)
X1







0
0
0
0
1
0
1
0
0
1



0
0
1
0
0
1
1
0
0
1


0
1
0
1
1
1
1
0
0
1


0
1
1
0
1
0
0
1
0
1
+


1
0
0
1
0
0
1
0
0
1


1
0
1
0
0
1
1
0
0
1


1
1
0
0
0
1
1
0
0
1


1
1
1
1
0
0
1
0
0
1









At least one of values s21(x) or s31(x) matches S11(x) and at least one of values s22(x) or s32(x) matches S12(x), which can easily be checked using table 4. Again, it is very easy to check by repeating the calculation or by using a commonly used synthesis tool that

y1=S11(x)= x1x2 x3x1( x2⊕x3)

y2=S12(x)= x1(x2 x3)

y3=S13(x)=x2⊕x3 

s21(x)= x1 x2x3

s22(x)= x1x2x3 

s31(x)=0

s32(x)=1

are possible realisations of the functions shown in table 4.
FIG. 5 shows a corresponding circuit arrangement which is fault-tolerant especially for input value x1x2x3=011 at the first two outputs y1 and y2. The circuit S for implementing the Boolean functions S11(x), S12(x) and S13(x) comprises gates 51, 52, 53, 54, 55, 56 and 57. The circuit for implementing the Boolean functions s21(x) and s22(x) comprises gates 58 und 59. The circuit for implementing the Boolean functions s31(x) und s32(x) comprises gates 510 und 511. The output of gate 510 still shows the value 0 and the output of gate 511 still shows the value 1. It can be recognised that hardware expenditure for realising the functions s21, s22 and s31, s32 is less than the expenditure for realising the functions S11 and S21.
The input line carrying the binary signal x1 is fed in non-negated form into the first input of AND gate 53, AND gate 510 and OR gate 511, respectively. In negated form x1 is fed into the first input of AND gate 52, AND gate 56, NAND gate 58, AND gate 59, respectively, and into the second input of AND gate 510 and OR gate 511, respectively. The input line carrying the binary signal x2 is fed into the first input of XNOR gate 51, into the second input of AND gate 52, into the first input of OR gate 55, into the first input of XOR gate 57, into the second input of NAND gate 58 and into the second input of AND gate 59. The line carrying the binary signal x3 is connected in non-negated form with the second input of XNOR gate 51, the second input of XOR gate 57, the third input of NAND gate 58, the third input of AND gate 59 and connected in negated form with the third input of AND gate 52 and the second input of OR gate 55.
The output of XNOR gate 51 is connected with the second input of AND gate 53, whose output is fed into the first input of an OR gate 54.
The output of AND gate 52 is connected with the second input of OR gate 54, whose output carries the value S11(x) and is fed into the first input of voter V1 512.
The output of OR gate 55 is connected with the second input of AND gate 56, whose output carries the signal S12(x) and is connected with the first input of voter V2 513.
The output of XOR gate 57 carries the value y3(x) which is output by circuit S. The output of NAND gate 58 carries the signal s21(x) and is connected with the second input of voter V1512, whilst the output of AND gate 59 carrying the signal s22(x) is connected with the second input of voter V2513.
The output of AND gate 510 carrying the here constant signal s31(x), is connected with the third input of voter V1512, whilst the output of OR gate 511 carrying the here constant signal s32(x) is connected with the third input of voter V2513. The voter V1512 outputs, at its output, the output value y1(x), whilst the voter V2513 outputs the output value y2(x) at its output. The voters V1512 and V2513, which perform a bit-by-bit majority decision, are combined in FIG. 5 to form one voter V 514. The output of XOR gate 57 is an output of the circuit carrying the output signal y3(x). This output is not implemented so as to be fault-tolerant.
The outputs of voters V1512 and V2513 carrying the signals y1(x) and y2(x) respectively are the circuit outputs which are implemented so as to be fault-tolerant. Voters V1 512 and V2513 performing a majority decision across the three inputs present at their inputs are combined to form one voter V 514 with 6 inputs and 2 outputs. Voter V1512 performs a majority decision across its values S11(x), s21(x), s31(x) present at its inputs and voter V2513 performs a majority decision across its values S12(x), s22(x), s32(x) present at its inputs.
The circuit of FIG. 5 is fault-tolerant at outputs y1 and y2 for input value 011. If this input is present at the inputs, this results in S11(0,1,1)=0, s21(0,1,1)=0, s31(0,1,1)=0 and S12(0,1,1)=1, s22(0,1,1)=1, s32(0,1,1)=1. If in case of a fault one of values S11(0,1,1), s21(0,1,1) or s31(0,1,1) is in error, such an error is tolerated due to the majority decision of voter V1512. Similarly: if in case of a fault only one of values S12(0,1,1), s22(0,1,1), s32(0,1,1) is in error, this error is tolerated by V2513.
For an input of 100 the result in a fault-free case is S11(1,0,0)=1, s21(1,0,0)=1 and s31(1,0,0)=0, resulting in voter V1512 generating the correct value y1(1,1,0)=1. Now, if a stuck-at-0 fault is present at the first input of AND gate 53, which carries the value x1=1, the first and second inputs of OR gate 54 show the value 0, resulting in this gate outputting the faulty value 0 at its output, with the result that voter V1512 processes the input 0,1,0 into 0. For an input of (1,0,0)εX2 the fault is not tolerated. Output y3 formed by the output of XOR gate 57 is not implemented so as to be fault-tolerant.
Analogously this leads to the circuit of FIG. 5 being fault-tolerant for an input of (0,1,1)εX1 at its second output, which carries the signal y2(x), since as already mentioned, S12(0,1,1)=1, s22(0,1,1)=1 and s32(0,1,1)=1.
FIG. 6 shows a further design of a combinational circuit arrangement. The combinational circuit S=S161 is supplemented by two combinational circuits s262 and s363. Combinational circuit S161 is the first combinational circuit component, combinational circuit s262 is the second combinational circuit component and combinational circuit s363 is the third combinational circuit component of the circuit arrangement according to the invention. The set of possible input values of circuit S is designated with X. The set of input values for which the circuit arrangement of FIG. 6 is fault-tolerant is designated with X1. X1 is a true or proper subset of X. The circuit arrangement is defined such that

S(x)=S1(x)=s2(x)=s3(x) for xεX1 with X1⊂X 

and

(S1(x)=s2(x)) or (S1(x)=s3(x)) for xεX 

wherein there exists a non-empty subset X2⊂(X\X1) so that

s1(x)≠s2(x) for xεX2.

Also present are a combinational circuit σ66 for realising a Boolean function σ(x) and a multiplexer MUX 65. The Boolean function σ(x) is defined as




  
    σ
    ⁡
    
      (
      x
      )
    
  
  =
  
    {
    
      
        
          
            
              b
              ⁢
              
                
              
              ⁢
              for
              ⁢
              
                
              
              ⁢
              x
            
            ∈
            
              X
              1
            
          
        
      
      
        
          
            
              b
              ⁢
              
                
              
              ⁢
              for
              ⁢
              
                
              
              ⁢
              x
            
            ∈
            
              X
              2
            
          
        
      
      
        
          
            arbitrary
            ⁢
            
              
            
            ⁢
            in
            ⁢
            
              
            
            ⁢
            all
            ⁢
            
              
            
            ⁢
            other
            ⁢
            
              
            
            ⁢
            cases
          
        
      
    
  




In this formula b is a fixed value which can be fixed to be 0 or 1. If xε(X\(X1∪X2)), then σ(x) can be specified arbitrary. An expert would define σ(x) for xε(X\(X1∪X2)) depending on the requirement by a CAD tool in such a way that circuit σ occupies as small an area as possible for implementing the Boolean function σ(x). The output of combinational circuit S161 carrying the signal S1(x) is fed into the first input of a voter V 64, at the second input of which is connected the output of combinational circuit s262 carrying the signal s2(x) and at the third input of which is connected the output of combinational circuit s363 carrying the signal s3(x). The output of voter V 64 carrying the signal m(x), which represents the majority of values of S1(x), s2(x) and s3(x) is connected with a first data input of multiplexer MUX 65, into the second data input of which is fed the output of combinational circuit S161 and whose data output carries the signal y(x). The control input of multiplexer MUX 65 is connected with the output of combinational circuit σ66 carrying the control signal σ(x).
In the following it is assumed that b=1 for the description of the mode of operation of the circuit arrangement of FIG. 6, in order to simplify the description. Analogously a description for b=0 is also possible. If xεX1, then σ(x)=1 and the multiplexer MUX 65 connects its corresponding 1-input with its output so that y(x)=m(x). Moreover S1(x)=s2(x)=s3(x) is applicable and voter V 64 determines the value m(x)=S1(x)=s2(x)=s3(x), which is fed to output y(x).
Individual faults of individual circuit components will now be considered. If only one of output values S1(x), s2(x) or s3(x) for xεX1 is faulty, this faulty value will be corrected by the majority decision of the voter and the correct value y(x) is output. If the control value σ(x) generated by circuit σ66 is equal to 0 which is faulty, the correct value S1(x) is forwarded to the output of multiplexer MUX 65 and y(x)=S(x) is again correct. If xεX2, then σ(x)=0 and the output of circuit S161 is forwarded to the output of multiplexer 65, so that y(x)=S1(x). Now if output value S1(x) is faulty, the faulty value is sent to the output of the circuit arrangement. This is the only case, in which a fault at one of the circuit components S 61, s262, s363, σ66 results in an error at the output value y(x). Further individual faults of the listed circuit components do not have any effect.
Any faults in voter 64 and in multiplexer 65 have nothing to do with the subject of the patent claims and are therefore not addressed here.
For example, if a fault-tolerance of the combinational circuit S with respect to a set of technical faults {φ1, . . . , φk}=Φ shall be achieved, the set X1 has to be selected such, that X1 contains all input values, for which an arbitrary fault φεΦ impacts upon the output behaviours of S1.
As a typical example for determining the Boolean functions σ(x), s2(x), s3(x) a combinational circuit S with S=S1(x)=S1(x1,x2,x3,x4)=x2x3x2(x1⊕x4)x1 x2x3x4 shall be considered, which shall be fault-tolerant for the set of input values X1={0000,0010,0111,1110,1111}. The first combinational circuit component with A1=a1=1 realises the Boolean function S1(x), the second combinational circuit component realises the Boolean function s2(x) and the third combinational circuit component realises the Boolean function s3(x).
Table 5, in the first four columns, shows the input values for x1, x2, x3, x4 and in the fifth column the functional values of the Boolean function S1(x). In the sixth column those lines are marked with +, for whose input assignments the circuit arrangement according to the invention shall be fault-tolerant. These are the first, third, eighth, fifteenth and sixteenth line. For the input assignments 0000, 0010, 0111, 1110 and 1111 corresponding to these lines the values of the Boolean functions s2(x) and s3(x) are identical and they also match with S1(x), so that

S1(x)=s2(x)=s3(x) for xεX1.

Next the still-to-be-determined functional values of the Boolean function s2(x) can be arbitrarily fixed in principle. In order to simplify realisation an expert would optimise s2(x) with the functional values fixed for xεX1, by applying a commonly used synthesis tool. To this end he would, for example, select all still undefined functional values of s2(x) as don't-care and thus optimise the given partially defined Boolean function, as is common.
For example, let it be assumed that s2(x) is defined as s2(x)=x2(x3x4). For this function the functional values are entered in column 8 of table 5. It will now be described how the Boolean function s3(x) can be defined.
xεX1 is defined as s3(x)=S1(x), as is the function s2(x). Thus: s3(0000)=S1(0000)=0, s3(0010)=S1(0010)=0, s3(0111)=S1(0111)=1, s3(1110)=S1(1110)=1, s3(1111)=S1(1111)=1. For the input values x, which are defined as s2(x)≠S1(x), s3(x)=S1(x) is set. Table 5 shows that the inequality s2(x)≠S1(x) for xε{1011,1100,1101} is satisfied. Thus: s3(1011)=S1(1011)=1, s3(1100)=S1(1100)=1 and s3(1101)=S1(1101)=0. The still-to-be-fixed values s3(x) may again be arbitrarily fixed at random. An expert would set all of the still-to-be-fixed values of s3(x) to be don't-care. In a concrete case these are the values for s3(0001), s3(0011), s3(0100), s3(0101), s3(0110), s3(1000), s3(1001), s3(1010) for which don't-care values can be set. Then he would optimise the described partially defined Boolean function using a commonly used CAD tool for example, as is common when circuits are designed.
















TABLE 5













s3 (x) =











 x1x2  









s2 (x) =
x1(x3  
σ(x) =


x1
x2
x3
x4
S1(x)
X1
X2
x2(x3   x4)
x2 x4)
 x1x2   x2x3







0
0
0
0
0
+

0
0
1


0
0
0
1
0


0
0
1


0
0
1
0
0
+

0
0
1


0
0
1
1
0


0
0
1


0
1
0
0
0

+
0
1
0


0
1
0
1
1


1
1
0


0
1
1
0
1


1
1
1


0
1
1
1
1
+

1
1
1


1
0
0
0
0


0
0
0


1
0
0
1
0


0
0
0


1
0
1
0
0

+
0
1
0


1
0
1
1
1

+
0
1
0


1
1
0
0
1

+
0
1
0


1
1
0
1
0

+
1
0
0


1
1
1
0
1
+

1
1
1


1
1
1
1
1
+

1
1
1









For example, let it be assumed that s3(x) was determined to be s3(x)= x1x2x1(x3x2 x4). The functional values of this function s3(x) have been entered into column 9 of table 5.
There now follows a description, how function σ is defined, which is illustrated in column 10 of table 5. In the lines marked with + in the column headed X1, the value of σ(x) equals 1. These are the first, third, eighth, fifteenth and sixteenth lines, which are allocated to the assignments 0000, 0010, 0111, 1110 and 1111. In the lines in which s2(x) and s3(x) are not equal, the value of σ(x) equals 0. These are the fifth, eleventh, twelfth, thirteenth and fourteenth lines, which are allocated to the assignments 0100, 1010, 1011, 1100 and 1101. All still-to-be-fixed values are again to be selected as arbitrary values or don't-care. As is common in circuit design, a CAD tool can again be used to define the function σ, which matches the values already fixed in column 10. For example, let it be assumed that σ has been defined to be σ(x)= x1x2x2x3. The functional values of this function have been entered in column 10 of table 5.
As a result, the following is true
If xεX1, then follows σ(x)=1 (lines 1, 3, 8, 15, 16)
If σ(x)=1, then follows S1(x)=s2(x)=s3(x) (lines 1, 2, 3, 4, 7, 8, 15, 16)
If s2(x)≠s3(x), then follows σ(x)=0 (lines 5, 11, 12, 13, 14)
If σ(x)=0, then follows s2(x)=s3(x)=S1(x) (e.g. line 9) or s2(x)≠s3(x) (e.g. line 5)
The set of input values X2, for which s2(x)≠s3(x), is marked with a + in column 7 headed X2. They form the set {0100,1010,1011,1100,1101}=X2. Furthermore the following applies:

(X\X1)={0001,0011,0100,0101,0110,1000,1001,1010,1011,1100,1101},

(X\X1)⊃X2,

X2={0100,1010,1011,1100,1101}

where X2 is a proper subset of X\X1. It should not be difficult for an expert to implement the corresponding Boolean functions as combinational circuits.
FIG. 7 shows a further design of a circuit arrangement for realising a fault-tolerant combinational circuit S, which realises a particularly effective fault-tolerance. In FIG. 7 the combinational circuit S is realised three times as S171, S272 and S373 with identical functions, resulting in

S(x)=S1(x)=S2(x)=S3(x) for xεX 

applying to all xεX from the set of possible input values.
X1 is the partial quantity of input values, for which a particularly high fault-tolerance shall be achieved. The three circuits S171, S272 and S373 are supplemented by the two combinational circuits s474 and s575, resulting in

S(x)=s4(x)=s5(x) for xεX1 

(S(x)=s4(x)) or (S(x)=s5(x)) for xεX 

wherein again a non-empty partial quantity X2⊂(X\X1) exists, resulting in

s4(x)≠s5(x) for xεX2 

The same input value x is present at each of the combinational circuits S171, S272, S373, s474 and s575. For i=1, 2, 3 the output of combinational circuit S, carrying the output signal Si(x) is fed into the i-th input of voter V 76. The output of combinational circuit s4 carrying the output signal s4(x) is fed into the fourth input of voter V 76, whilst the output of combinational circuit s5 carrying the output signal s5(x) is connected with the fifth input of voter V 76. The voter V 76 with 5 inputs outputs the value m(x)=y(x) at its output, wherein m(x) is the value, which most frequently occurs at the 5 inputs of voter V 76.
If xεX1, in a fault-free case, 5 identical values are present at the input of voter V 76 and up to two faulty values are tolerated by the circuit in FIG. 7 as output of S171, S272, S373, s474 and s575. If xεX2, in a fault-free case, 4 identical values are present at the input of voter V 76 as output of S171, S272, S373, s474 and s575 and one faulty value is tolerated by the circuit in FIG. 7.
For xεX1 the circuit arrangement of FIG. 7 has the fault-tolerance characteristics of a fault-tolerant system, wherein the original system is five times implicated, and for xε(X\X1) of at least of a system where the original system is triplicated, wherein expenditure is less than for the system which is five times implicated.
The first combinational circuit component S171 realises the function S1(x), the second combinational circuit component s474 realises the function a4(x) and the third combinational circuit component s575 realises the function s5(x). These circuit components are supplemented by two further combinational circuit components S272 and S373, which also realise the same function, respectively, as the first circuit component.
FIG. 8 shows a further embodiment of a fault-tolerant circuit arrangement. The circuits S181, s282 and s383 are identical with circuits S131, s232 and s333 of FIG. 3. In FIG. 8 a voter is present three times as voter V184, V285 and V386.
The output of combinational circuit S1(x) carrying the signal S1(x) is simultaneously fed into the respectively first inputs of voters V184, V285 and V386. The output of combinational circuit s282 carrying the signal s2(x) is simultaneously fed into the respectively second inputs of voters V184, V285 and V386, whilst the output of circuit s383 carrying the signal s3(x) is connected with the respectively third inputs of voters V184, V285 and V386. The voters V184, V285 and V386 output the majority signals m1(x), m2(x) and m3(x) respectively. If one voter is faulty, most of the majority signals are correct.
FIG. 9 shows a further fault-tolerant circuit arrangement. The circuit arrangement of FIG. 9 comprises a circuit S 96, which is fault-tolerant with respect to the input set X1 and which has a circuit T 95 arranged upstream of it. The circuit S 96 comprises the circuits S191, s292 and s393 and a voter V 94, as described with reference to FIG. 3.
The circuit T 95 processes input values u from a quantity U of inputs into output values T(u), which form the set of output values W of circuit T 95. k, k≧2 stands for the word width of the output of circuit T 95, which is simultaneously connected with the m-bit wide inputs of circuits S191, s292 and s393, wherein m=k. The set of possible inputs in principle of circuit S 96 is X={0,1}k, i.e. the set of all k-digit binary vectors.
If the circuit T 95 is designed in such a way that W is a proper subset of X, then X1⊂W is selected in FIG. 9, and the circuit S is fault-tolerant for all input values from the set X1, wherein X1 is a proper subset of W.
The output of circuit T 95 is connected simultaneously with the inputs of circuits S191, s292 and s393. The output of circuit S191 is connected with the first input of a voter V 94 with three inputs. The output of circuit s292 is connected with the second input of voter V 94 and the output of circuit s393 is connected with the third input of voter V 94, which at its output outputs a majority signal m(x).
A circuit T 101, which processes input values u=u1u2ε{00,01,10,11} into output values T(u)=T1(u)T2(u)=x1x2ε{00,01,11}ε{00,01,10,11}, is shown in FIG. 10. The set {00,01,11} of output values of circuit T 101 is a proper subset of the set X={0,1}2={00,01,10,11} of all possible input values of circuit S 104. It is thus possible, to select X1 as a subset of W={00,01,11}, for example as X1={00, 01}, for which the circuit S 104 is a fault-tolerant circuit according to the invention.
The circuit T 101 comprises an AND gate 102 and an OR gate 103, into which the input values u=u1u2ε{00,01,10,11} are input and which are processed by the circuit T 101 into the output values T(u)=T1(u)T2(u)ε{00,01,11}. The input of circuit T 101 carrying the first component u1 of the input value u is connected with the respectively first input of gates AND102 and OR103, into whose respective second input is fed the input of circuit T 101 carrying the second component u2 of input value u. The AND gate 102 outputs the first component T1(u) and the OR gate 103 outputs the second component T2(u) of output value T(u).
The features of the invention disclosed in the above description, in the claims and in the drawing can be important both individually and in any given combination to the implementation of the invention in its various embodiments.

## Claims

1. An electronic circuit arrangement for processing binary input Values xεX of word width n(n>1), comprising:
a first combinational circuit component configured to process the binary input values x to form a first binary output value of word width a1(a1≧1) and to provide the first binary output value at the output of the first combinational circuit component, the output of the first combinational circuit component being provided with a number of binary outputs A1(A1>1), wherein A1≧a1,
a second combinational circuit component configured to process the binary input values x to form a second binary output value,
a third combinational circuit component configured to process the binary input values x to form a third binary output value, and
a majority voter element, the input of which, for receiving the respective binary input values, is connected with the outputs of the first, second and third combinational circuit components, the majority voter element being configured to provide a majority signal at its output in dependence on the received binary output values,
wherein the second and third combinational circuit components are configured, as regards faults during processing of the binary input values x in the first combinational circuit component, to process, for the first binary output value of word width a1,
binary input values of a true non-empty subset X1 of the set of binary input values X in a fault-tolerant manner and
binary input values of a further non-empty subset X2 of the set of binary input values X in a non-fault-tolerant manner, the further non-empty partial quantity X2 being different from the true non-empty subset X1;
wherein the second and third combinational circuit components are designed to incorporate the following features:
in a fault-free case the second binary output value of the second combinational circuit component and the third binary output value of the third combinational circuit component are equal to the first binary output value of the first combinational circuit component, for all binary input values of the non-empty proper subset X1;
for all binary input values from the further non-empty subset X2 the second binary output value of the second combinational circuit component and the third binary output value of third combinational circuit component are non-equal, and
for all binary input values of the subset X1 the following is true:
for each bit of the first binary output value of word width a1: at least the second binary output value of the second combinational circuit component or at least the third binary output value of the third combinational circuit component is equal to the first binary output value of the first combinational circuit component.

2. Circuit arrangement according to claim 1, wherein the second combinational circuit component is configured to process the binary input values x such that the second binary output value is equal to the first binary output value.

3. Circuit arrangement according to claim 1, wherein further combinational circuit components are configured to process the binary input values x to form the first binary output value, and the output of which is respectively connected to an input of the majority voter element.

4. Circuit arrangement according to claim 1, comprising further majority voter elements the input of which, for receiving the respective binary output value, is connected with the output of all combinational circuit components and which are respectively configured, depending upon the received binary output values, to provide a majority signal at their output.

5. Circuit arrangement according to claim 1, wherein the respective input of all combinational circuit components is serial-connected with an output of a further circuit component, wherein the further circuit component is configured to process binary input values uεU to form binary output values W which, at least partially are different from the binary input values xεX, wherein X1⊂W.

6. Circuit arrangement according to claim 1, further comprising:
a further combinational circuit component configured to process the binary input values x to form binary control signals, and
a multiplexer element,

wherein
the output of the further combinational circuit component carrying the binary control signals is connected with the control input of the multiplexer element,
a first data input of the multiplexer element is connected to the output of the first combinational circuit component, and
a second data input of the multiplexer element is connected with the output of the majority voter element.

7. Circuit arrangement according to claim 1, wherein the binary input values of non-empty subset X1 form a subset of binary input values, so that for a set Φ of faults φ1, . . . , φk occurring in the first circuit component, the following is true: S(x)≠S(φ,x) for xεX1, wherein S(φ,x) is the binary output value of the first combinational circuit component, if the fault φεφis present and the binary input value x is input.

8. Circuit arrangement according to claim 1, wherein X2=(X\X1).

9. Circuit arrangement according to claim 1, wherein the binary output value of the second circuit component is to be 1 and wherein the binary output value of the third combinational circuit component is to be 0 for the binary input values from the further non-empty subset X2.