FR2460567A1 - DEVICE FOR REDUCING IRRATIONAL CODES WITH MINIMUM FORM - Google Patents

Abstract

THE INVENTION CONCERNS THE TECHNOLOGY OF CALCULATIONS. THE DEVICE WHICH IS THE OBJECT OF THE INVENTION IS CHARACTERIZED IN THAT EACH FUNCTIONAL CELL 1 INCLUDES A REVERSE SIGNAL INPUT THE REVERSE SIGNAL INPUT OF THE L-ME FUNCTIONAL CELL BEING CONNECTED TO THE INFORMATION OUTPUT OF THE (L-1) -ME FUNCTIONAL CELL, N BEING THE FORMAT OF THE IRRATIONAL BASED CODE, 10, 1, 2, ..., (N-1); P1. THE DEVICE IN QUESTION CAN BE USED IN PARTICULAR IN COMPUTERS, DIGITAL INFORMATION PROCESSING SYSTEMS, IN DIGITAL INSTRUMENTS AND SYSTEMS FOR REDUCTION OF IRRATIONAL BASED CODES TO THE MINIMUM FORM.

Description

The present invention relates to the technique of calculations and in particular

  a device for the reduction of irrationally based codes to the minimum form. It is susceptible of application, in particular, in computers, digital information processing systems, in digital instruments and systems for the reduction of codes based on

irrational to the minimal form.

  It is known that any natural number N can be represented as n = -l 1 =) N = E a, tP (l (1)

1 = 0

  one is the format of the code, Y (1) is a p-number of Fibonacci, and the p numbers of Fibonacci are defined, for a given p> O integer, by the following recurrence relation: O for <O p ( 1) = 1 for = O (2) t (11i) + Op (lp-1) for 10 for p = O, the Fibonacci p codes generalize the representation

  classical binary, and for p = oo, they identify themselves with the "unitary" code.

  The evolution of this numeration is the p-code "gold". A p-code of "or" of a real number is called its writing as a sum of powers of the proportion p of "gold", where PC {1i, 2,3 ..., oo} A = 1 (3) o (1 <(0, 1) is the binary digit of the 1st rank of code pd "'or" C1 is the weight of the 1st rank (1-me power of proportion pd " "or"); l is the proportion pd "gold" constituting the real root of the equation: p xp + i = xp + (4) Thus for p = 1 i1 = 1 +2 the factor = - is here

  proportion of "gold" (hence the code name (3)).

  The proportion p of "gold" has the following fundamental property: n n-1 + n-p-i () p = p p

  that oniti, immediately from the equation (M).

- 1 -

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  The Fibonacci p codes and the pd '' or codes are irrationally based codes in the ratio: (, (n + i) lim P + ap (6) n-oo Lp (n) p The main feature irrationally based codes are their redundancy, that is to say that each number A has several notations in the irrationally based codes For example, for p = 1, the number 8 can be written in the Fibonacci code (p = 1) next: Weight 13 8 5 3 2 1 1 Fibonacci Code 1 0 0 0 0 0 0

0 0 1 1 0 0 0 8

  ≥8 0 0 1 0 1 o0 1 or in code 1 of "or": Pd "3" 2 1 & -1 -2 -13 Weight O0 (CK 0 ("'1 1 111111e Code 1d"' Or " 1 OOO 1 OOO 1)

0 1 1 0 1 0 0 0 1 = 8

0 1 1 0 0 1 1 0 1

0 1 0 1 1 1 1 0 1

  An important notion of irrational code theory is that of the normal or minimal form, which is understood to be an irrationally based code of the number A, in which any group consisting of p + 1 digits

  consecutive contains no more than one in one.

  The reduction of the irrational based code to the minimal form is called "normalization of the irrationally based code". For p = 1, the normalization is done by carrying out all the operations of convolution of the bits of the code. By convolution of the bits in 1 of the code an_1 and an_2 to the n-me bit

  in 0 years = 0, we mean the complementation (or replacement by the negation) -

n bits, ie: year-1 year-2

0 1 1

1 0 0

  The convolution operation is designated t I. I.

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  The inverse operation of the convolution is called development and has for symbol, .., It is essential to insist that neither the convolution nor the development of the bits do not change the coded number A, this

  which results from the fundamental property (5).

  The convolution of the "golden" code consists in performing all the operations of convolution of the bits. For example, for the code of the proportion of "gold": 3 "2 <1 0 1 2 Weight

0 1 0 1 0 1 1

0 1 0 1 1 0 0

0 1 1 0 0 0 0

t I

1 0 0 0 0 0 0

  The development of the "golden" code consists in carrying out all the bit development operations. For example, for the code of proportion p d "gold":

3 2 0- 1 2-3

  DC "2 K10" 1 (1 21 CK Weight i 0 1 0 0 0 0

1 0 0 1 1 0 0

  0 1 1 i 0 1 1 There is a unique device that achieves the reduction to the minimal form of the irrationally based code, namely the Fibonacci p-code, which comprises homogeneous functional cells, each having an input and a outputting information for writing and reading the figurative joinative codes of the number A, information convolution inputs, a prepositioning input, a convolution control input, and a signal output of convolution, related according to the algorithm

operation of the device.

  All the functional cells have the same assembly comprising a

  toggle and logical elements "AND" and "OR".

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  However, the existing scheme suffers from a functional ambiguity

  the flip-flops (known as the "strokes" effect), possible when reducing to the minimum form of a certain p-Fibonacci code. Said ambiguity of operation can come from the excursion of the technological parameters of the elements forming part of the functional cell and cause non-simultaneity of operation. For example, during the reduction to the minimum form of the Fibonacci code 1 from the number 10, written as follows Weight 13 8 5 3 2 1 1 Cell number 6 5 4 3 2 1 0 Code 10 0 1 1 1 1 0 The convolution towards the fifth functional cell can give rise to a situation where, following the drift of the technological parameters of the elements of the fourth functional cell, its flip-flop takes the state 0 more rapidly than that of the third functional cell. It is then

  that the condition of convolution to the fourth functional cell is created

  nelle. The result is the following code: v 1 1 0 0 involving the convolution operation to the sixth functional cell. Finally, we have the code 1 0 0 0 0 0 0, that is to say that the reduction to the minimum form is false. By generalizing, we can say that the races can appear in all 2n- Y (In) cases of reduction of the

initial code to the minimal form.

  It should be noted, moreover, that the existing device is limited in its functional possibilities, because it does not make it possible to operate on the codes p of

  Fibonacci as convolution and development.

  The present invention therefore aims at an irrationally based code reduction device with the minimum shape, designed to expand the functional possibilities, by allowing the summation of the codes pd "'or11, the storage of reliable information, the conversion of the powers of the proportion of "gold" written in a p-code diluted pulse count code, a better operational reliability resulting from the sequential execution of row-by-row convolution, i.e. cell

functional to another.

  This problem is solved by means of a device for reducing irrationally based codes to the minimum form, of the type comprising a number n of homogeneous functional cells equal to that of the numbers.

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  each having at least one input and one information output, a positioning input, two convolution information inputs, a convolution control input and a signal output of convolution, the 1-th functional cell having its convolution signal output connected to the positioning input of the (lp-1) me functional cell, and its information output connected to one of the information inputs of convolution of the (1 + 1) -me functional cell and the other convolution information input of the (l + p + 1) -memory functional cell, characterized, according to the invention, in that each functional cell possesses an inversion signal input and that the invert signal input of the 1-me functional cell is connected to the information output of the (1-1) -multiple functional cell, where n is the

  irrationally based code length, 1 = 0, 1, 2, ..., (n-1); p = 1.

  It is reasonable that in the device using for irrational codes the Fibonacci code p and the proportion code p'd "'or", according to the invention, each functional cell from 1 = 1 contains a latch to counting input having its inverting output connected to one of the inputs of an AND logic element, its other inputs respectively connected to the convolution information inputs and to the convolution control input of the same functional cell, that the output of the logic element AND and the non-inverting output of the flip-flop are respectively connected to the convolution signal output and to the information output of the same functional cell, as the inputs 1, 0 and counting of the latch of the 1-me functional cell are respectively connected to the information input, the convolution positioning input and the inversion signal input of the same functional cell and that the functional cell representative of the rank

  the least significant of the code is performed with a flip-flop.

  It is preferable, in order to effect the development of the codes, according to the invention, that each functional cell of the device additionally has two development signal inputs, a reset input (RAZ), an inhibition input of convolution, a development inhibition input and a development signal output, that the 1st functional cell has its development signal output connected to one of the (1-1) developing signal inputs; me functional cell and to the other development signal input

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  of the (lp-1) -me functional unit, that its inhibition inputs and its convolution inhibition inputs are respectively united in two common points respectively constituting the input of inhibition of the development and the input convolution inhibition device for the reduction of irrational based codes to the minimal form. It is necessary, in order to allow the development operations in the device according to the invention, that each functional cell comprises a development inhibition gate, a convolution inhibition gate, a logic element or a gateway 1. flip-flop and a logic element OR to reset the flip-flop, that one of the inputs of the door

  of inhibition of development is connected to the inverting output of the

  flip-flop, that its other input and its output respectively constitute the inhibition input of the development and the output of development signal of the same functional cell, that both inputs of the inhibition gate of the convolution respectively form the convolution inhibition input and the invert signal input, that its output is connected to the counter input of the flip-flop which has its input 1 connected to the information input and development signal inputs of the same functional cell through the logical OR element of the flip-flop, and its input 0 connected to the reset input (RAZ) and to the convolution positioning input through the logical element OR of

reset the scale.

  It is useful, to allow the control of the accuracy of the functioning

  according to the invention, that each functional cell of the device -

  has a control output and has an AND logic control element which has its two inputs respectively connected to the output and to the convolution information input of the same functional cell, and

  that its output forms the control output of the functional cell.

  It is advantageous from the point of view of the extension of the functional possibilities, that in the device using as code irrationally based the code of the proportion pd "'or", according to the invention, that the 1-me functional cell (to from 1 = 2) has a functional input and a logic OR delay element which has its inputs connected to the remaining inputs of the logic element OR of setting of the flip-flop, and that the third input of the logic element OR of the flip-flop is connected to the functional input and to the second signal input of

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  development of the first functional cell through the logical element

OR late.

  The present invention makes it possible, in addition to improving the reliability of devices for reducing to the minimum form irrationally based codes, namely Fibonacci p codes and codes of the proportion pd "gold", to simplify the functional cell and perform additional operations of converting the powers of the code of the proportion pd "'gold", counting pulses and summing the codes of

the proportion p of "gold".

  The invention will be better understood and other purposes, details and advantages

  it will appear better in the light of the explanatory description which

  will follow various embodiments given solely by way of non-limiting examples with references to the accompanying non-limiting drawings in which - Figure 1 shows the block diagram of the device for the reduction of irrationally based codes to the minimum form, realizing the convolution of the joined codes, according to the invention; FIG. 2 is the block diagram of the device carrying out the convolution and the development of the contiguous codes, according to the invention; FIG. 3 is the block diagram of one of the particular embodiments of the functional cell, according to the invention; FIG. 4 is a block diagram of another particular embodiment of the functional cell, allowing the extension of the functional possibilities of the device for the case of the conversion of the

  codes of the proportion of "gold", according to the invention.

  FIG. 1 shows a particular embodiment of the device for reducing the irrational based codes to the minimum form for p = 1 and n = 5, where n is the code format (the irrational code function is

  made by the Fibonacci code i or the code i of the proportion of "gold").

  The device comprises n, that is to say five, homogeneous functional cells 1, each 1-me cell (ie 1 = 2) has an information input 2 intended for writing information in the form of a code number, an information output 3 enabling the reading of the information on the state of the functional cell 1, the first and second convolution information inputs 4 and 5 which receive the information on the state (1-1) -me and (lp-1) -me, that is to say the (1-2) me, functional cells 1. Each 1-me

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  functional cell 1 comprises a positioning input 6 which receives a reset i of the 1-th functional cell 1; a convolution control input 7 which, if it goes to 1, allows for eventual convolution; a convolution signal output connected to the positioning input 6 of the (l-p-1) -th functional cell 1 (this output delivers a 1 to the realization of the convolution condition); an inverting input for receiving the inversion signal of the functional cell 1 during the convolution operation. The convolution signal output of the 1-th functional cell 1 is connected to the convolution positioning input 6 of the (lp-1) -me (i.e. me) functional cell 1; the information output 3 of the 1-th functional cell 1 is connected to the first convolution information input 4 of the (l + 1) -th functional cell 1 and to the second information input 5 of the + p + 1) -me (i.e. (1 + 2) -me) -functional cell 1. The convolution control inputs 7 of all the functional cells 1 are connected to a "bus" "(common set of interconnection wires) forming the control input of the entire device which receives a 1 when there is a Fibonacci p-code or a p-code of the" gold "proportion to reduce to the minimum form. The information outputs 3 of all the functional cells i constitute a multi-bit information output of the device, the number of bits being equal to n. The information inputs 2 of all functional cells 1 form a multi-bit information input of the device for

  write the information on the number represented in an irrationally-based code

nelle.

  It should be noted, moreover, that the 1st functional cell 1 comprises an inverting signal input, connected to the information output 3 of the (1-1) -th functional cell and intended for the inversion signal. imposing the

  change of state of the 1-me-functional cell 1.

  Each 1-me functional cell (from 1 = 1) contains a count input latch 8. In all the functional cells 1, except that representative of the least significant digit of the code, the inverting output 9 of the flip-flop 8 is connected to one of the inputs of the logical AND convolution element 10. The other inputs of the logical AND convolution element 10 are respectively connected to the convolution information input 4, to the information input convolution 5 and at the command input of

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  convolution 7 of the functional cell 1. The output of the logical AND convolution element 10 forms the convolution signal output of the 1-th functional cell 1. The output of the logical AND convolution element 10 goes to 1 in the case where the flip-flop 8 is in the O state and the first and second convolution information inputs 4 and 5, as well as the convolution control input 7, are at 1. The non-inverting output of the

  flip-flop 8 constitutes the information output of the functional cell 1.

  The inputs 1 and 0 of the flip-flop 8 are respectively connected to the information input 2 and to the convolution positioning input 6 of the

functional cell 1.

  The functional cell 1 representative of the least significant digit of the code is in the form of a flip-flop 11. As indicated in FIG. 1, the functional cells 1 represent two low-order digits (1 = O and 1 = 1). and a most significant digit (l = nr-1) have some "in the air" inputs. Thus, in the figurative functional cell 1 of the first digit, one of the convolution information inputs is not effective; in representative functional cells 1

  third and fourth digits, this is the case

  6, and in the most significant functional cell, it is the convolution information input 4 which is in this case. However, the functional cells 1 are of universal design and if the device has a greater number n of numbers, the growth of the functional cell chain 1 must take place on the side of the most significant digit (l = n-1 ), so that all the inputs of the third and fourth functional cells 1 are affected. But the design of the functional cell

  1 figurative of the low weight figure remains the same as in Figure 1.

  FIG. 2 shows another particular embodiment of the device for the reduction of the irrationally based codes to the minimum form for p = 1 and n = 6, the function of irrationally based codes being

  made by the Fibonacci code i and the p code of the proportion of "gold".

  The device comprises six homogeneous functional cells 1 and its difference with respect to that of FIG. 1 is that each functional cell 1 has a first and second development signal input 12 and 13, which receive a 1 imposing the development operation and setting the functional cell 1 to 1; a reset input (reset) 14 whose passage to 1 causes the setting of the functional cell to 0; a convolution inhibition input 15, intended

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  the convolution inhibition signal; a development inhibition input 16 for the development inhibition signal; a development signal output connected to the development inputs 12 and 13 of the (1-1) -me and (1-p-1) -m functional cells 1. This output goes to 1 when the development condition is realized. The inhibition inputs of the convolution 15 of all the functional cells 1 are connected to a common "bus" (interconnection wires) of inhibition of the convolution of the device which, when passed to 1, prevents any convolutions in the device. The inhibiting inputs of the development 16 are connected to a common "bus" of inhibition of the development of the device which, once at 1, prohibits possible developments in the device

  for the reduction of the codes to the minimal form.

  As can be seen in Figure 2, some functional cells 1 have some of their inputs "in the air"; thus, in the functional cell 1 figurative of the low-order digit (1 = 0) the inhibition inputs of convolution and expansion 15 and 16 are unused: the development signal output and the development signal input 12 ; in the functional cell 1 of the first digit, these are one of the convolution inhibition inputs 15 and the signal output of

  development that are "in the air"; in the functional cell representing

  in the high order digit (l = n-1) the development signal inputs 12 and 13 are not affected; in the figurative functional cell of the (n-2) -me digit, it is input of development signal 13 which is unused. In order for the device to process a larger number of digits, the growth of the functional cell chain 1 must occur on the high-order digit side, in which case all of said

  inputs and all of said outputs will be effective.

  FIG. 3 shows a particular embodiment of the 1-me (ie 1 = 2) functional cell 1 comprising a development inhibition gate 17, a convolution inhibition gate 18, a logic element OR 19 at 1 of the flip-flop and a logic element OR 20 of setting

at 0 of the rocker.

  One of the inputs of the inhibit gate of the development 17 constitutes the inhibition input of the development 16, its second input is connected to the inverting output 9 of the flip-flop 8, and its output forms the output of the development signal . Development inhibit gate 18 - h1 2460567 serves to prohibit the transfer of a 1 from the inverted output 9 of flip-flop 8 to the development signal output in the presence of an inhibition signal at the input of inhibiting the development 16. The inhibition gate of the convolution 18 is intended to prevent the passage of a 1 from the information output 3 of the (1-1) -th functional cell 1 (figure at the entrance inversion signal during the convolution operation, provided that an inhibition signal is applied to the inhibition input of the convolution 15. The output of the logic element OR 19 1 of the flip-flop (FIG. 3) is connected to the input 1 of the flip-flop 8. The inputs of the logic element OR 19 for setting the flip-flop are intended for the signals coming from the first input of the development signal 12 , information input 3 and the second development signal input 13. These are these inputs which ensure the writing of the initial information in the flip-flop 8 and its reset 0 to development, the output of the logic element OR 20 is connected to the reset input (reset) of the flip-flop 8. The inputs of the logic element OR 20 receive the signals from the input of

  resetting (reset) 14 and convolution positioning input 6.

  It is these inputs that move the flip-flop 8 to the 0 state to development

  and convolution, respectively.

  The inhibition gate of the convolution 18 has its output 21 connected to the counting input of the flip-flop 8. The functional cell 1 also comprises an AND logic control element 22 which has one of its inputs connected to the output 5, its second input connected to the first convolution information input 4, its output forming the output

  control 23 of the functional cell 1.

  The logical AND control element 22 is used to test, with regard to the minimum form, the irrationally based code. It delivers a 1 when the

  1-me and (1-1) -me functional cells 1 are in state 1.

  FIG. 4 represents a particular embodiment of the 1-th functional cell 1 of the device carrying out the conversion of the single code of the proportion p of "gold". In contrast to the particular embodiment of FIG. 3, each 1-th functional cell 1 from 1 = 2 here comprises a logic OR delay element 24, which has one of its inputs connected to the second signal input of FIG. 13, and the other, to a functional input 25. The second development signal input 13 is connected to the third input of the logic element OR 20, the input

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  functional 25 being joined to the remaining input (the fourth) of

the logical element OR 20.

  The functional input 25 is intended for the information signals 1 to the power pulse code conversion rate of the proportion pd "gold" in code of the proportion pd "'gold", as well as to the speed regimes. counting pulses representative of the proportion code pd "'or"

  and summation of the p codes of the proportion of "gold".

  At the convolution regime, the irrational code reduction device at the minimum form behaves as follows. For example, if you want to reduce to the minimum form the number 5 written in Fibonacci code 1 other than minimum, in the form Weight 5 3 2 1 1 Number of the cell

functional 4 3 2 1 0.

  Fibonacci Code 1 0 1 0 1 1 Through information inputs 2 (Figure 1), this code is provided to flip-flops 8 and rocker 11 of the functional cells of the third and first digit and the zero digit. At the appearance of an i at the control input of the device, the logical element AND 10 of the 1-me functional cell 1, which receives I information outputs 3 (1-1) -me and (lp-1) -me functional cells 1 and the inverting output of flip-flop 8 analyzes the possibility of convolution. In the case considered, the convolution condition (the presence of a 0 at the information outputs 3 of the 1-me functional cell 1 and 1 at the information outputs 3 of the (1-1) -me and (lp -1) -me functional cells 1) is

  satisfied for the second functional cell.

  A 1 appearing at the output of the AND logic element 10, that is to say at the convolution signal output of the second functional cell 1, is applied to the convolution positioning input 6 to set to 0 the

  flip-flop 11 of the functional cell representative of the zero digit.

  This functional cell 1 delivers by its information output 3 a 0 which arrives by the inversion signal input to the counting input of the flip-flop 8 of the first functional cell 1 to set it to 0. The first cell The functional unit then sends via its information output 3 a 0 to the counting input of the flip-flop 8 of the second functional cell 1, which takes the state 1. The first convolution is complete.

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  and its result is the code 0 1 O 0, which satisfies the convolution condition for the fourth functional cell 1. The convolution signal output of this functional cell 1 goes to I and everything happens next as above:

Q 1 1

0 1 0

0 0 0

1 0 0

  It follows that the initial encoding combination 0 1 0 1 1 becomes 1 0 0 0 0, which corresponds to the minimum writing form of the number 5 in the Fibonacci code 1. The duration of the signal 1 at the control input of the device must be far greater than that required by all the possible convolutions. After the convolution, the information on the minimum Fibonacci code 1 obtained is read at the information outputs 3 of the functional cells 1 of the device. The reduction to the minimum form of the code of the proportion p of "gold" is effected in a similar manner. It must be emphasized that with the proposed mechanism for the reduction of irrational codes to the minimal form, there is no need to fear

  ambiguity of operation regardless of the Fibonacci p code to be processed.

  Said device is designed so that the convolution operation is sequentially done from the (1-p-1) -me digit to the (1-1) -me digit and the (11) -me digit to the 1st digit. Once the condition of convolution realized for 1-me, (1-1) -me and (1-p-1) -me functional cells 1, it is the flip-flop 8 of the (1-p-1) - functional cell 1 which is the first to take the state 0. This functional cell provides a 0 by its information output to the counting input of the flip-flop 8 of the (1-1) -memory functional cell 1 for set it to 0, which results in the writing of a 1 in the flip-flop of the 1-me cell 1. The simultaneity of operation of the flip-flops 8 materializing

  three digits are no longer necessary.

  In the scheme of development of the irrationally based code, the device behaves as follows. It will be assumed that the device displays code 1 of the following proportion of "gold": e2 MoqO & 12 3

1 0 1 0 0 0

  The convolution inhibition input 15 (FIG. 2) receives from a block of

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  external control (not shown) a level of inhibition, and the input

  of inhibition of development 16, a level of validation.

  If now, by means of a pulse distributor (not shown), a sequence of 1 is applied to the reset inputs (RAZ) 14 of all the functional cells i, starting with the one translating the weight (, a 1 applied to the reset input (reset) 14 of the functional cell l characteristic of the weightCO comes through the logic element OR 20 set to 0 the flip-flop 8. Said flip-flop 8 delivers by its inverting output 9 a 1 which arrives through the development inhibition gateway 17 to one of the development signal inputs 12 of the functional cell 1 representative of the weight 0 (1, and to the other development signal input 13 of the functional cell 1 which materializes the -2 weight 0. The same i arrives through logical elements OR 19 to

  inputs 1 of the flip-flops 8 of the functional cells 1 to set them to 1.

  This results in the display, by the device, of the following code

& 2 0 (1 "1 OT2 & 3

1 0 0 1 1 0 new state.

  Subsequently, at the arrival of a 1 at the reset input (reset) 14 of the functional cell 1 translating the weight C2, the behavior of the device will be identical to that just described, and we will have the following code: o (2 "k1 & k 1c23

1 0 0 1 1 0

O 1 1 1 1 0 new state.

  On this, the development stops.

  The addition of a logical AND control element 22 to each functional cell 1 makes it possible to organize the storage of the information so that the device is able to identify failures of the flip-flops 8

and 11.

  It will be assumed that the device receives a minimum code of the "gold" proprotion, for example 32 oi 1 o2 o3 O i O l O O

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  It should be noted first of all that the writing of information in the device is controllable. In fact, if the writing of the minimal code of the proportion pd "'or" does not meet the definition of the minimum code, the error of writing of the code will be recognized with the presence of 1 at the control output 23 d At least one of the functional cells 1. The storage of the minimum code of the proportion p of "gold" recorded is also controllable. It is necessary for this purpose to suppress the inhibitory potential at the entry of inhibition of the development 16, and to inhibit the entry of inhibition of the convolution 15. If it is now supposed that the latch 8 of the functional cell 1 the material Dk passes from the state 1 to the state 0 under the action of a parasite, it results in the appearance, at the inverting output 9 of the flip-flop 8 of said functional cell 1, a 1 which, via the gate 17, is applied to the development signal output. Through the first input of the development signal 12 and the logic element OR 19 for setting the flip-flop, this 1 arrives at the input 1 of the flip-flop 8 of the functional cell O 1 representative of the weight e0 to go to state 1. It should be noted, moreover, that the same 1 is applied, through the second development signal input 13 and the logic element OR 19, to the input 1ide-la flip-flop 8 of the functional cell 1, which materializes the weight 0k 1. But this latch 8 is already in the state 1 and must therefore keep it. The device will now display the following "golden" proportion code

2 21O 1

  0 0 1 t 0 0 which is not the normal code. Also the control output 23 of the functional cell 1 representative of the weight C0 passes to 1, which indicates the existence of an error. In this way, the device whose functional cell 1 is given in FIG. 3 makes it possible to recognize all the failures of flip-flops 8 of type 1 -> 0. It should be noted in this connection that there is also a significant rate of failures of the type 0 ---> 1

(rv9950 for n720).

  The device whose functional cell is the subject of FIG. 4 makes it possible to organize the storage of information so that the failures

  type 1-90 are not destructive of digital information.

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  This is achieved by introducing the logical element OR of delay 24 further.

  one of the inputs is now connected to the second development signal input 13. The same input is joined to the third input

  of the logic element OR 20 of setting the flip-flop.

  It is now assumed that the device receives the same code of proportion dl "or" o (2 Lo 1 3

0 1 0 1 0 0

  Inhibition input of the convolution 15 is inhibited and the inhibition input of the development 16 is no longer inhibited. If the flip-flop 8 of the functional cell 1 representing the weight Ct passes again from 1 to 0 under the effect of a parasite, it appears at the output of the development signal of said functional cell a 1 which is applied to the first one. development signal input 12 of the functional cell 1 representative of the weight Ct0, and which sets its flip-flop 8. The same 1 arrives at the second development signal input 13 of the functional cell 1, which materializes the DC weight . The effect will be the following through the logic element OR 20 O setting of the flip-flop, this 1 will switch the flip-flop 8 to the state O to appear then, through the door passante 17 of inhibition of development, at the

  development signal output of the functional cell 1 represents

  0 1. As a result, 1, as described above,

  flip-flops 8 functional cells 1 materializing the weights C-2 and OC3.

  The same 1 from the second development signal input 13 of

  the functional cell 1 representative of the weight OC 1, appears, by -

  via the logic element OR delay 24, after a time t counted from the instant of setting of the flip-flop 8 of the same functional cell to the input of the logic element OR 19 and , therefore, at the input 1 of the same flip-flop 8, to reset it to 1. The device now displays the code 02 <1 0 Cl 2 - -3

O 0 1 1 1- 1

  Then, the inhibit input of the development 16 is inhibited. while at the inhibition input of convolution 15 is suppressed the potential

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  inhibition. After that, upon the application of 1 to the control input of the device, said code of the proportion of "gold" will be reduced to the minimum form as described above, i.e.

"2 C" 1 D (O & 2 3

0 <0 <J <(1 &

0 0 1 1 1 1

o o 1 o 1 1 o o o o o o o

0 1 0 0 0 0

0 1 0 1 0 0

  The joined codes obtained are identical to the start codes and, consequently, the restoration of the code is correct. In this way, if the probability of failures of the type 1 -> 0 is much greater than that of the type 0 --- 1, the proposed device can be used advantageously for the correction of errors, that is to say that all the disturbances of the type 10 are correctable by the device. Otherwise, the device may

serve as error testers.

  The addition of the logic element OR 24 with delay t to the functional cell i of FIG. 4 makes it possible to significantly extend the functional possibilities of the entire device, which thus becomes capable of converting the code to count pulses of the powers of the proportion of "gold" in code of the proportion p of "gold", to count the pulses and to write the result of the count in the code of the proportion

  of "gold", and to sum the codes of the proportion of "gold".

  At the rate of conversion of the pulse count code of full power of the proportion of "gold" in code of the proportion pd "'or", the n ni n device'translates the sum 0 <(+0 (+. + Q in proportion code

,,,, ......... N times ..

  Golden". This is how, for n = O, the device 1 converts more

  of units 1 + _1 + .. in the code of the proportion of "gold".

  N times The operation at such a regime requires the inhibition of the inhibition input of the development 16 and the suppression of the inhibition of the inhibition input of the convolution 15. Then, it is necessary to apply a series of pulses briefly at the functional input of the functional cell 1 corresponding to the power of the proportion of "gold" to be converted. The duration of said pulses

18 2460567

  can not exceed the delay t introduced by the OR delay element 24 their number must be equal to a number N. A short pulse applied to the functional input 25 of the functional cell i considered appears at the input 0 of the latch 8 with a delay t due to the logic element OR 20. After having a delay 2 t in the logical element OR delay 24 and the logic element OR 19 set 1 of the flip-flop, this pulse appears at the input l of the flip-flop 8. If the flip-flop 8 was then in the state 1, it first goes to the state 0 and, after a time t, to the state 1. In this case the gate 17 delivers (development signal output) a 1 (the development inhibition gate 17 being on) respectively to the first development signal input 12 and the second development signal input 13 of the functional cells 1 which materialize the low-weight figures. This 1 sets the flip-flops 8 of said functional cells 1. If the flip-flop 8 of the functional cell 1 representative of the respective power of the proportion of "gold" to be converted, was in state 0, it takes the state 1 after a time 2 t. Then it is necessary to apply to the control input of the convolution of the device a sufficiently delayed control signal with respect to the count pulses to allow the completion of transient processes related to the development of the "golden" ratio code, and sufficiently long to ensure the accomplishment of the transitional processes related to the convolution of the proportion code

Golden".

  It should be emphasized that to allow convolution, the development inhibition input 16 must be inhibited and the inhibition input

convolution 15 validated.

  At the pulse counting regime, all flip-flops 8 of the device are initially in state 0, the inhibiting input of the development 16 is inhibited and the inhibition input of the convolution 15 is enabled. The first counting pulse arrives at the functional input 25 of the functional cell 1 representative of the weight e 0 to set to its latch 8. In the device will be recorded the following code

2 (1 O 2

1 = 0 0 1 0 0 0

  The device then receives at its convolution control input signals 1 providing convolution (the parameters of said signals are

given above).

- 19- 2460567

  Initially, the second count pulse arrives through the logic element OR 0 for setting the flip-flop and switches flip-flop 8 to state 0. The effect is the appearance of an I at development signal output which, after having passed through the first development signal input 12 and the logic element OR 19 set to 0 of the flip-flop, makes state 1 to flip-flop 8 of the functional cell i materializing the weight 0 (1, through the second development signal input 13, the delay logic OR element 24 and the logic element OR 19, the said 1 causes the flip-flop 8 of the functional cell I to be in the I state The second counting pulse is applied via the logic OR delay element 24 and the logic element OR 19 to setting the flip-flop at the input 1 of the latch. flip-flop 8 of the functional cell 1 representative of the weight C 0. This pulse, whose appearance n at the input 1 of the flip-flop 8 is delayed by 2 t with respect to its appearance at the functional input 25, sets the flip-flop 8. In this way, the second counting pulse will make the device go to next state:

12 ç 2 O3

  2 = 0 0 1 i 1 0 Now a convolution validation 1, applied to the control input of the device, will trigger convolution as before, i.e. the device will have the following state :

1 0 1 2 R3

2 = 0 1 0 0 1 O,

  translating the minimal form of representation of the number 2 in the code

d "tor".

  It is easy to see that after the appearance of the third and fourth count pulses, the states of the device will alternate as follows: X2 1U C0 -1c2 É3 3 = i 0 i 0

1 0 0 0 1 0

  4 = 1 0 1 0 i 0 The proposed device has a good self-checking power. The result

- 20 - 2460567

  definitive operation of said device is always the minimum code of the porportion of "gold". If, as a result of electronic failures, the device does not reduce the code to the minimum form, the immediate manifestation would be a 1 permanently present at the control output 23 of one of the functional cells 1. For example, if in one of the functional cells 1 produced a break in the output of the logical AND convolution element 10, which would lead to the following situation:

0 1 1

  after the application of a 1 to the control input of the device the convolution would not take place. The effect would be the permanent presence

  from a 1 to the control output 23 of the functional cell 1 corresponds to

  you. In this way, the convolution process is itself a process

control.

  The process of summing numbers in the "golden" proportion code will be examined by considering, by way of example, the operation of a nine-digit device which can be realized in a manner analogous to

  six-figure device of Figure 2.

  Said device acts as a cumulative serial adder as follows. It is assumed that the sum of two 4 + 4 numbers in the "golden" code must be added. For this purpose it is first necessary to write in the device the code of "gold" of the number to increase: ol4 ot ç COC1 2 C & 3 4

0 0 1 0 1 0 1 0 0

  after which it is necessary to successively apply each of the digits in 1 to the respective functional inputs of the device. If the summation takes place on the side of the low-weight digits, it proceeds as follows: 1) application of a 1 of the second row "4V3 C, <2 - <6UO k 2 3 0 0 1 0 1 0 1 0 0 summation

+0 0 O O O O 1 0 0

0 0 1 0 1 0 1 1 '1

  35.kL. 0 0 1 0 1 1 0 0 1 eductionducode to I Jf code reduction to 1 1 00 0 0 0 1 the minimum form

0 1 0 0 0 0 0 0 1

* - 21- 2460567

  2) application of a 1 of the fourth rank

0 1 0 0 0 0 0 0 1

+ f summation

00 0 0 1 0 0 0 0

0 1 1 0 1 0 0 0 1

  3) application of a 1 of the sixth row O43 this M 0 & o2 3 -a

0 1 0 0 1 0 0 0 1

+ summation

0 0 1 0 0 0 0 0 0

0 1 1 0 1 0 0 0

  0 1 i0 i o0 o 1 i reduction of the code to 1 D 0 0 1 0 - 0 0 1 the minimum form

The summation is thus finished.

  In this way, said device for the reduction of irrationally based codes to the minimal form has high reliability and extensive functional possibilities; it constitutes the main organ of the devices handling the Fibonacci p codes and the codes of the proportion of "gold"; it can serve as a basis for all the main subsystems of digital instrumentation, which then become capable of a "natural" self-control. Improving the informational reliability of digital instruments for irrationally based codes is the advantage

  practical part of the proposed scheme.

  Of course, the invention is not limited to the embodiments described and shown which have only been given to

  as an example. In particular, it includes all the means

  technical equivalents of the means described, as well as their combinations, if these are executed according to his spirit

  and implemented in the context of the claims.

- 22 - 2460567

Claims (6)

  1. Device for the reduction of irrationally based codes to the minimum form of the type comprising n homogeneous functional cells whose number corresponds to that of the digits of the code and each of which has at least one information input and one information output, a convolution positioning input, two convolution information inputs, a convolution control input and a convolution signal output, the first functional cell having its convolution signal output connected to the positioning input of the (lp-1) - me functional cell, its output of information connected to one of the convolution information inputs of the (1 + 1) -me functional cell and the other input of convolution information the (l + p + 1) -memory functional cell, characterized in that each functional cell comprises an inverting signal input, the inversion signal input of the 1-me functional cell being connected e to the output information of the (1-1) -me functional cell, n is the irrational based code format, 1 = 0, 2. Device according to claim 1, characterized in that the function of irrationally based codes is fulfilled by the Fibonacci code p and the code of the proportion pd "'or", that each functional cell (from 1 = 1 ) comprises a flip-flop having a counting input and whose inverting output is connected to one of the inputs of a logical AND convolution element whose other inputs are respectively connected to the convolution information inputs and to the control input for convolution of the same functional cell, that the output of the convolution logic element AND and the non-inverting output of the flip-flop are respectively connected to the convolution-signal output and to the information output of the same functional cell , that the inputs 1, O and counting of the flip-flop of the 1-me functional cell are respectively connected to the information input, to the convolution positioning input and to the inversion signal of the same functional cell, the functional cell representative of the weight   weak of the code being realized in the form of a rocker.   3. Device according to one of claims 1 and 2, characterized in that   each functional cell further has two development signal inputs, a reset input (RAZ), a - 23_ 2460567   the convolution, a development inhibition input and a development signal output, that in the 1-me functional cell the development signal output is connected to one of the development signal inputs of the ) -me functional cell and the other development signal input of the (lpl) -me functional cell, the development inhibition inputs and convolution inhibition inputs are respectively brought together in two common points constituting respectively a development inhibition input and a convolution inhibition input of the device for the reduction of the codes to   irrational basis to the minimal form.   4, Device according to one of claims 1, 2 and 3, characterized in   each functional cell contains a gate for inhibiting the development, a gate for inhibiting convolution, a logic element OR for setting the scale and a logic element OR for setting the scale to zero; one of the inputs of the development inhibit gate is connected to the inverting output of the flip-flop, and its other input and output respectively constitute the inhibit input of the development and the output of the development signal of the same functional cell , that both inputs of the convolution inhibition gate respectively represent the inhibition input of the convolution and the invert signal input, that its output is connected to the input of counting of the flip-flop which has its input 1 connected to the information input and to the development signal inputs of the same functional cell via the logic element OR of setting of the flip-flop, its input e O being connected to the reset input (RAZ) and the convolution positioning input via the logic element OR set to O of the rocker.   5. Device according to one of claims 1, 2, 3 and 4, characterized   in that each functional cell has a control output and   an AND control logic element whose inputs are respectively connected   information output and to one of the convolution information inputs of the same functional cell, its output forming the output   control of the functional cell.   6. Device according to one of claims 1, 2, 3, 4 and 5,   characterized in that the irrationally based code function is fulfilled by the code of the proportion p of "gold", that the 1st functional cell (from 1 = 2) has a functional input - 24 - 2460567   and a logic OR delay element which has its inputs connected to the remaining inputs of the logic element OR of the flip-flop, the third input of the logic element OR of setting of the flip-flop being connected to the functional input and at the second development signal input of the 1-me functional cell via the logic element OR late.