# Method for conversion of code of remainder classes system to voltage

FIELD: computer science.

SUBSTANCE: method includes forming of two supporting harmonic oscillations and where t - time of production from supporting oscillation of harmonic oscillation and from harmonic oscillation - oscillation and determining multiplication result integral for these oscillations: where T_{u} - integration interval.

EFFECT: higher precision, higher speed of operation.

2 dwg

The invention relates to the field of automation and computer engineering and can be used in the design of devices for converting digital code in the system of residual classes (JUICE) in the voltage in units of pairing different items computational and information-measuring systems.

The known method (analog) conversion code JUICE voltage [1, s-240], which consists in converting the numbers in the JUICE in the positional number system (PSS) and the subsequent formation of the obtained positional code voltage by summing the currents is directly proportional to the weights of the bits of the position code on the common load resistance [2, s-211].

The disadvantage of this method is poor performance, due to the need for more code translation JUICE in MSS.

The closest in technical essence (the prototype of the present invention) is a method based on the well-known [1, p.31; 3, p.35-39, p.77-78] the method of obtaining the position code number And code (α_{1}that α_{2},... ,α_{N}in JUICE:

where

[• ] is the integer part of the number; m_{i}- a set of relatively Prime positive integers;

μ_{i}
- weight of orthogonal basis obtained from the solution of the comparison (μ_{i}M_{i})mod

r_{A}- rank of A, which represents a non-negative integer indicating how many times the range JUICE - M was exceeded during the transition from the representation of a number to the JUICE to his positional representation.

This method of code conversion JUICE in voltage is [4, p.23-24] in the calculation of the modules m_{i}that works discharges α_{i}code number And JUICE on the weight of orthogonal bases μ_{i}these discharges - β_{i}=(α_{i}thatμ_{i})mod m_{i}where m_{i}- base JUICE i=1,2,... N, the summation for the total resistance of the load currents is directly proportional to the fraction values β_{i}/m_{i}and the subtraction of the voltage obtained by passing the sum of these currents through the load resistance, voltage, directly proportional to the rank of r_{A}.

The disadvantage of the prototype low speed, as when converting the JUICE into a voltage necessary to calculate the rank of r_{A}. Known algorithms to obtain the rank of [3, p.78-82; 4, p.23-24] requires the extra cost of equipment and are only for N steps, where N is the number of bases in the JUICE.

The aim of the proposed method is to improve the performance of the PE the perspective of samples computing and information-measuring systems for various purposes.

The technical result is expressed in faster execution of code conversion JUICE in tension.

This objective is achieved in that in the known method, including calculating the modules m_{i}that works discharges α_{i}code number And JUICE on the weight of orthogonal bases μ_{i}these discharges - β_{i}=(α_{i}thatμ_{i})mod m_{i}where m_{i}- the Foundation of the JUICE; i=1,2,... N, optionally form two reference harmonic oscillations u_{01}(t)=Ucos(ω · t) and u_{02}(t)=Usin(ω · t), where U and ω respectively the amplitude and frequency of harmonic oscillations; t - time, obtained from the reference oscillation u_{01}(t) harmonic oscillation u_{1}(t) by L shifts phases on the

where j=1,2,... L; L is the integer part of the result of dividing the number N by 2, and from harmonic oscillations u_{02}(t) get a harmonic oscillation u_{2}(t) by (N-L) phase shifts

where k=(L+1), (L+2),..., N, and define the integral works of these fluctuations:

moreover, the value of u_{u}whenT_{u}>(2... 3)T and 0≤ And<<M equals to the value of the number A, where T_{u}- the integration interval; T - period of the harmonic oscillations;

usnot invention is based on the use of the periodicity of the harmonic function, similar to the ring of classes of deductions integer modules.

Since in the present method there is no need to compute the rank of a number, there is an increase in performance transformation code, the JUICE in the voltage.

It is known that

where p=1,2,3,...

May be formed of two harmonic oscillations u_{01}(t)=Ucos(ω t) and u_{02}(t)=Usin(ω t) with amplitude U and the frequency ω .

If the initial phase of the harmonic oscillations u_{01}(t) move L time value

where L is the integer part of the result of dividing the number N by 2; j=1,2,... L, and the initial phase of the second harmonic oscillations u_{02}(t) move (N-L) times the value of the

where k=(L+1), (L+2),..., N, then shifts the data harmonic oscillations will be described the corresponding expressions

As

and in turn

on the basis of (3) and (5) we get

Similarly, taking into account the expression (4), we obtain the formula

the second term which is converted to the form

Accordingly, based on (4) and (7), we obtain

If harmonic oscillations (6) and (8) to multiply and integrating, we arrive to the following expression:

where[3, p.36, formula (1.30)].

Here the approximate equality in (9) follows from the assumption that when ω >>1 and T_{u}≥_{}(2... 3)T, where T is the period of the harmonic oscillation u_{1}(t) and u_{2}(t), the integral of the Raman component of the compositions of harmonic oscillations with a total frequency significantly less than the integral of the Raman component difference (zero) frequency.

By appropriate choice of the set of bases JUICE m_{i}you can always ensure that the amount was much less than the range of number representation in the JUICE - M, that is, 0≤ And<<M, Then (9) can be represented in the following approximate proportions:

which shows that if

will be provided an approximate equality

For example, if

that is the argument of sin(• ) coincides with its value to the fourth decimal.

Considering the above, in EMA formation of the code JUICE voltage will be equal to the sum of the time delays τ
ϕ harmonic vibrations (3) and (4) in L devices of the phase shift and the integration time T_{u}works fluctuations u_{1}(t) and u_{2}(t), i.e. tΣ ≈ τ ϕ +T_{u}.

Since the delay harmonic oscillations on a time interval equal to the duration of its period corresponds to a phase shift angle of 2π , the time delay in the formation of any of the L phase shifts is assumed to be the period of the frequency of the reference harmonic oscillations

Then τ ϕ ≈ L· T.

As mentioned above, T_{u}≥_{}(2... 3)T. let us Take T_{u}=3T. Therefore, the time for receiving the voltage from the code of JUICE equals

At the conclusion of the formula (12) were assumed to be

For example, when the frequency of the reference harmonic oscillations 100 GHz and N=8 time tΣ ≈ 7· 10^{-11}with that commensurate with the maximum possible switching time digital logic element [5, s], and, therefore, significantly less time calculating the rank of r_{A}in arithmetic devices based on semiconductor logic elements required to obtain from the code JUICE voltage using the prototype.

Figure 1 shows a structural diagram of a device that implements the proposed method pre is obrazovaniya code JUICE in voltage,
where 1_{1}-1_{N}information input device, 2_{1}-2_{N}- the display device 3 - generator harmonic oscillations, 4 - Phaser angle5_{1}-5_{N}- managed phasers, 6 - analog multiplier, 7 - integrator, 8 - output device.

Information inputs 1_{1}-1_{N}connected to the inputs of the respective display devices 2_{1}-2_{N}the outputs are connected with the second inputs of the corresponding managed phasers 5_{1}-5_{N}while the output of the oscillator 3 is connected directly to the first input of the controlled phase shifter 5_{i}and through the phase shifter angle4 - with the first input of the control phase shifter 5_{L+1}with the controlled phase shifter 5_{j}connected to the first input of the controlled phase shifter 5_{(j+1)}where j=1,2,... L-1, and the output of the controlled phase shifter 5_{k}connected to the first input of the controlled phase shifter 5_{(k+1)}where k=(L+1),(L+2),..., N-1, and the output of the controlled phase shifter 5_{N}connected to the first input of the analog multiplier 6, a second input connected to the output of the controlled phase shifter 5_{L}while the output of the analog multiplier 6 is connected to the input of the integrator 7, the output of which is an output device 8.

Consider the operation of the device. N information inputs 1_{1}-1_{N}the device comes unitary codes α_{i}the corresponding digits in A code JUICE, where i=1,2,..., N. since the weights of the orthogonal bases μ_{i}constants, in the display devices 2_{1}-2_{L}by an appropriate change of the input data bus regarding the output is a unary transformation α_{j}→_{}(α_{j}thatμ_{j})mod m_{j}=β_{j}where j=1,2,... L, a in the display devices 2_{L+1}-2_{N}- unary transform α_{k}→_{}(m_{k}-α_{k}thatμ_{k})mod m_{k}=(m_{k}-β_{k})mod m_{k}where k=(L+1),(L+2),... N.

As an example of the display devices 2_{1}-2_{N}figure 2 shows a diagram of a display device that implements the conversion α → (α · 3)mod5.

Unitary codes numbers β_{j}and (m_{k}-β_{k})mod m_{k}coming to the second inputs of the respective managed phasers 5_{j}and 5_{k}where j=1,2,..., L; k=(L+1),(L+2),... N. In managed phasers are set corresponding phase shifts

and

After undergoing harmonic oscillations from the output of the generator 3 through the respective phase, the output is probleemiga Phaser 5_{
L}set the total RAID phases

and the output of the controlled phase shifter 5_{N}- RAID phases

In the result of multiplication in an analog multiplier 6 of harmonic oscillations with these shifts phases and subsequent integration in the integrator 7, the output 8 of the device produces a voltage directly proportional to

whichand 0≤ A<<M will be equal to the number of A.

Example. Let N=5; m_{1}=11; m_{2}=7; m_{3}=5; m_{4}=3; m_{5}=2; A=50;α_{1}=A mod m_{1}=6; α_{2}=1; α_{3}=0; α_{4}=2; α_{5}=0 (And=(6, 1, 0, 2, 0)); μ_{1}=1; μ_{2}=1; μ_{3}=3; μ_{4}=2; μ_{5}=1.

After the unitary transformation code numbers α_{1}that α_{2}that α_{3}that α_{4}and α_{5}in the display devices 2_{1}-2_{5}on the second inputs of managed phasers 5_{1}-5_{5}accordingly enter the following values unitary code (α_{1}thatμ_{1})modm_{1}=6; (α_{2}thatμ_{2})modm_{2}=1; (m_{3}-α_{3}thatμ_{3})modm_{3}=0; (m_{4}-α_{4}thatμ_{4})modm_{4}=2 and (m_{5}-α_{5}thatμ_{5})modm_{5}=0. In problemih the phasers 5_{
j}and 5_{k}where j=1 and 2, and k=3,4 and 5, respectively, are the following phase:and ϕ_{5}=0.

After undergoing harmonic oscillations from the output of the generator 3 through the respective phase, the output of the controlled phase shifter 5_{2}set the phase shift equal to

and the output of the controlled phase shifter 5_{5}set the phase shift equal to

In the result of multiplication in an analog multiplier 6 harmonic oscillations from the output of the controlled phase shifter 5_{2}-

u_{1}(t)=

with the oscillation output of the controlled phase shifter 5_{5}-

u_{2}(t)=

and its integration in the integrator 7, output 8 is formed voltage

Whenget the

Because the code JUICE you can only view of integers [3, p.12], from the above example you can see that clearly can be decided on the number And equal to 50.

Sources of information

1. Cherniavsky A.F., and other high-Speed methods and is istemi digital information processing. - Mn.: The Belarusian state University, 1996. - 376 S.

2. GITIS AI, Piskunov E.A. Analog-to-digital converters. - M.: Energoizdat, 1981. - 360 C.

3. Akutski IA, yuditsky DI Machine arithmetic in residual classes. - M.: Owls. radio, 1968. - 440 S.

4. Abramson, ETC, Avrov O.M., Lapkin L.Y. Coding of electrical quantities in the system of residual classes. // Avtometriya, No. 2 (62), 1975, p.23-29.

5. Akaev A.A., Maiorov S.A. Optical methods of information processing. - M.: Higher. HQ., 1988. - 237 S.

The way the code conversion system of residual classes (JUICE) into a voltage, comprising calculating by the modules m_{i}works discharges α_{i}code number And JUICE on the weight of orthogonal bases μ_{i}these discharges - β_{i}=(α_{i}μ_{i})mod m_{i}where m_{i}- the Foundation of the JUICE; i=1,2,...N, characterized in that it further form two reference harmonic oscillations u_{01}(t)=U· cos(ω · t) and u_{02}(t)=U· sin(ω · t), where U and ω respectively the amplitude and frequency of harmonic oscillations; t - time, obtained from the reference oscillation u_{01}(t) harmonic oscillation u_{1}(t) by L shifts phases on thewhere j=1,2,...L; L is the integer part of the result of dividing the number N by 2, and from harmonic oscillations u_{02}(t) get a harmonic oscillation u_{2}(t) by (N-L) shifts the phase
where k=(L+1), (L+2),..., N, and define the integral works of these fluctuations:moreover, the value of u_{u}whenT_{u}>(2...3)T and 0≤ And<<M equals to the value of the number A, where T_{u}- the integration interval; T - period of the harmonic oscillations;

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