Digital Differential Analyzer With an Increment Output Function

This invention relates to a digital differential analyzer and more particularly to a digital differential analyzer of the kind in which the arithmetic operations for the differential analysis of data are performed in accordance with a stored program.

As is commonly known, the digital differential analyzer (DDA) is used to solve various linear and nonlinear differential equations at high speed and yet with a relatively high degree of precision and to produce signals representing complicated curves or complicated curved surfaces. The DDA basically performs an integrating operation but it can perform various kinds of operations when the operation logic contained therein is properly modified. Further, if the operation logic is controlled by a computer with a given stored program, as described in U.S. Pat. No. 3,555,514 entitled "Digital Computer Instruction Sequencing to Carry Out Digital Differential Analysis" and U.S. Pat. No. 3,274,376 entitled "Digital Differential Analyzer in Conjunction with a General Purpose Computer", a DDA arranged to perform proper processings of data can be designed. The DDA is a digital apparatus; however, if the operation logic thereof is properly controlled, it can serve as an operator with a function equivalent to that of an analog operator such as an integrator, a counter, an adder, a servo, and a decision maker. Accordingly, the processes controlled by a conventional analog operator may also be controlled by using the DDA with the operation logic controlled.

Compared with a control system exclusively used for analog operation, a control system using the DDA is inferior to the former in the response speed but superior to the same in accuracy of the control. Further compared with a control system using a usual digital computer for control, the DDA control system is comparable with the digital computer control in high accuracy in control but superior thereto in the response characteristic.

As described above, the DDA is useful in its performance, but the expression of input and output used in the operation of the DDA is different from that in the so-called general purpose computer (GPC) as follows:

Now assume that y is a time-variable quantity and z is a function of y, and that it is desired to obtain a value of z with variation of the value of y. Generally, any of the DDA and the GPC performs a specific operation repeatedly at a predetermined iteration timing in order to obtain such a value of z.

In the operation of the GPC, an instant value of y is latched at the beginning of each iteration cycle and subjected to a specific operation which directly produces the value of z corresponding to the input value of y. That is, in the GPC, inputs of y.sub.0, y.sub.1, . . . y.sub.i are latched successively at the 0-th, 1st, 2nd, . . . i-th iteration cycles, respectively, and as the results of the repeated operations, there are produced outputs of z.sub.0, z.sub.1, . . . z.sub.i, respectively.

On the other hand, the DDA uses, as inputs, y.sub.0, y.sub.1 -y.sub.0, y.sub.2 -y.sub.1, . . . y.sub.i -y.sub.i-1, respectively in the 0-th, 1st, 2nd, . . . i-th iteration cycles, and produces, as outputs, z.sub.0, z.sub.1 -z.sub.0, z.sub.2 -z.sub.1, . . . z.sub.i -a.sub.i-1, respectively. Hereinafter, the value of such y.sub.0, y.sub.1 . . . or z.sub.0, z.sub.1 . . . will be called a whole value, while the value of such y.sub.1 -y.sub.0, y.sub.2 -y.sub.1 . . . or z.sub.1 -z.sub.0, z.sub.2 -z.sub.1 will be called a value of an increment or simply an increment. For this reason, it is troublesome in its handling in practical use. More specifically, when the DDA is used with an automatic process control system, it is required to apply to the DDA operator only increments extracted from a whole value of each of various signals obtained from the process and to accumulate the increments resulting from its operation thereby to reconstruct the whole value to be applied as a control signal to the process.

Of those problems, the reconstruction of the whole value from increments, or the conversion of the increments into the whole value can be easily realized by using the contents of an integrand register, as called hereinafter "Y register", of the DDA which stores an integrand y, since the Y register holds an accumulation of increments operated. The problem to still be solved is how to obtain increments of various signals accurately and simply. The techniques so far proposed are: to provide hardware between the process and the DDA for producing increments of whole values of various signals from the process; or to input whole values of various signals from the process, as integrands y into the Y registers of a specific DDA operator thereby producing integration of y with respect to time, which is applied to a y increment generator composed of a combination of specific DDA operators so as to produce the increments.

The former technique is uneconomical because of use of the special and additional hardware and, when the number of signals from the process from which increments are derived are large, the additional hardware may be more expensive than the DDA proper. Also, an increased number of parts of the hardware which necessarily causes the reliability to degrade is undesirable for the process control system which inherently needs a fairly higher reliability.

The latter technique needs a plurality (e.g. 3 to 4) of DDA operators. Further, it is difficult to stably obtain increments when the control system is designed with an intention of a high response speed. Conversely, when the system is designed so as to stably obtain increments, the response speed is slow. Thus, it is very difficult to obtain an optimum compromise between the requirements of stable increment derivation and high speed response.

In order to eliminate the defects of the prior arts, the invention provides a DDA having a function of converting a whole value into an increment value.

FIG. 1 shows a block diagram of an embodiment of a DDA according to the invention.

FIG. 2 shows a circuit diagram of a logic circuit as an example used in the circuit in FIG. 1.

FIG. 3 shows an equivalent block diagram for explaining the operation of an integrator.

FIGS. 4 and 5 show the symbols of an integrator and a servo which are constructed by DDAs.

FIGS. 6 and 7 show Karnaugh maps for studying a construction of a part of the logic circuit shown in FIG. 2.

FIGS. 8 and 9 show the symbols for illustrating the addition function of the DDA according to the invention and that of the conventional DDA.

FIG. 1 shows a block diagram of a DDA which is an embodiment according to the invention. In FIG. 1, input units I.sub.1 to I.sub.n receive input signals in a given format from a process to be controlled (not shown). Y registers Y.sub.1 to Y.sub.n are coupled with the input units I.sub.1 to I.sub.n, by way of a data bus DB.sub.1. An adder AD is coupled with the Y register Y.sub.1 to Y.sub.n by way of a data bus DB.sub.2, and to an incremental register (referred to as ".DELTA.Z" register"), as described later and an incremental sign register (referred to as ".DELTA.Z' register"), as also described later, by way of data buses DB.sub.3 and DB.sub.4. The output of the adder AD is coupled with the Y register via a data bus DB.sub.5. A latch register LH.sub.1 latches the data in a given Y register at a given timing under control of a control unit SPC. A decoder DC produces logic `0` onto a signal line C.sub.6 only when the data latched in the Y register is 0 and produces logic `1` when the data takes any other value. An arithmetic logic unit ALU.sub.1 receives the output of the latch register LH.sub.1 via a data bus DB.sub.8, the output of a latch register LH.sub.2 which latches any one of the data in R registers R.sub.1 to R.sub.n via a data bus DB.sub.9, increment data via data buses DB.sub.3 and DB.sub.4, and a signal for providing an increment .DELTA.t to effect a time integration through a data bus DB.sub.6, respectively, and performs a given operation under control of the control unit SPC. A bit shifter SF shifts the incremental data coming through the data bus DB.sub.3 to a bit position to which the incremental data is added in accordance with a signal from the control unit SPC which indicates the bit position of the data latched in the latch register LH.sub.2 to which the incremental data is added. Another arithmetic logic unit ALU.sub.2 performs a given operation of a signal applied thereto in accordance with a control signal delivered from the control unit SPC. A selector SL receives the output of the latch LH.sub.2 through the data bus DB.sub.9, and the add/substraction outputs of the arithmetic logic units ALU.sub.1 and ALU.sub.2 through the data buses DB.sub.10 and DB.sub.11, respectively, and selects one of them under control of a signal applied from the control unit SPC. The R registers R.sub.1 to R.sub.n are coupled with the selector SL through a data bus DB.sub.12. The R register and the latch register LH.sub.2 are coupled with each other through a data bus DB.sub.13. A logic circuit LC serves as a .DELTA.Z increment generator, receiving the signal C.sub.6 from the decoder DC and further signals C.sub.1 to C.sub.3 to C.sub.5. In those signals, signals C.sub.1 and C.sub.5 represent sign bits of the data latched in the latch registers LH.sub.1 and LH.sub.2. The signal C.sub.3 becomes logic `1` when the data of the latch registers LH.sub.1 and LH.sub.2 are equal to each other, i.e. when A=B holds. The signal C.sub.4 designates a sign bit of the operation result of A.+-.B. .DELTA.Z' and .DELTA.Z" are the .DELTA.Z and .DELTA.Z' registers which operate in accordance with the output of the logic circuit LC and a control signal from the control unit SPC. Output units O.sub.1 to O.sub.n produce the data held in the Y register as a process control signal under control of a signal from the control unit SPC. The control unit SPC stores a predetermined program for performing a given function of the DDA to issue necessary control signals and timing signals.

On the basis of the aforementioned construction of the DDA, the operation of the DDA, when it acts as an integrator which is the basic function of the DDA, will be described briefly. Let it be assumed that the Y register Y.sub.2 and the R register R.sub.2 are used. The control unit SPC delivers commands for the use of those registers to the related components of the DDA, so that the related gates of the data buses associated with the components are controlled at given timings. As a result, the DDA operates with a function of an equivalent circuit as shown in a block diagram of FIG. 3. As shown, the circuit is comprised of an adder AD, the arithmetic and logic unit ALU.sub.1 (it basically operates as an adder, in this case), the Y register Y.sub.2 storing the result of the operation by the adder AD and the R register R.sub.2 storing the result of the operation by the unit ALU.sub.1. As shown, the circuit does not use the unit ALU.sub.2 in this case. In the figure, .DELTA.y.sub.1 to .DELTA.y.sub. n are minute increments (referred to as input increments) of n input variables. At the ith operation, the following integrand y is stored in the Y register Y.sub.2 ##EQU1## where a suffix i designates a value of the result of the i-th operation and i-1 designates a value of the operation result of the (i-1) operation preceding to the i-th operation.

In accordance with the equation (1), the increments of input variables are accumulated, and the result is stored as a whole value of the integrand y in the Y.sub.2 register.

An integral I of the integrand y with respect to an integral independent variable x can be obtained according to the well-known method of piecewise mensulation. That is, the integral I of a curve y=f(x) can approximately be given by the equation ##EQU2## where I.sub.1 indicates the integration from the first to the i-th division and y.sub.i .DELTA.x.sub.i indicates the measurement of the i-th division.

In the equation (2), if the value of .DELTA.x is sufficiently small, an integral with a sufficient accuracy in practical use can be obtained. Assuming that u is the minimum quantitized unit of the integral independent variable x and, .DELTA.x is defined as follows:

when x increases by u, .DELTA.x.sub.i =+1

when x decreases by u, .DELTA.x.sub.i =-1

when a change of x is below u, .DELTA.x.sub.i =0 then, the equation (2) is

Therefore, a multiplier for calculating y.sub.i .DELTA.x.sub.i in the equation (2) may be omitted by using a control pulse, in place of .DELTA.x.sub.i, for controlling the operation. The operation of the equation (3) is performed by the arithmetic logic unit ALU.sub.1 shown in FIG. 3 under control of the .DELTA.x.sub.i pulse. The integrated value I.sub.i is stored in the R register R.sub.2 as r.sub.i. Since the capacity of the R register R.sub.2 is finite, however, an overflow might occur in the R register R.sub.2. Hence, y.sub.1 and r.sub.i are constrained within scopes -1.ltoreq.y.sub.i <+1 and 0.ltoreq.r.sub.i <+1, respectively, and the overflows thereof are related to the increment .DELTA.z.sub.i of the output variable as follows: ##EQU3## As seen from the equation (4), when the value r.sub.i-1 +y.sub.i to be stored in the R register R.sub.2 is above 1, the increment of .DELTA.z.sub.i =+1 is produced and the value of overflow (remainder) exceeding +1 is loaded as r.sub.i in the R register R.sub.2. When 0.ltoreq.r.sub.i-1 +y.sub.i <1 which is within the limitation of value to be stored in the R register R.sub.2, the value of r.sub.i-1 +y.sub.i is stored as r.sub.i in the R register R.sub.2 and .DELTA.z.sub.i is made 0, i.e. .DELTA.z.sub.i =0. When r.sub.i-1 +y.sub.i is smaller than 0, .DELTA.z.sub.i =-1 is outputted and r.sub.i-1 +y.sub.i +1.gtoreq.0, i.e. difference between r.sub.i-1 +y.sub.i and -1, is loaded as r.sub.i to the R register R.sub.2. .DELTA.z.sub.i is a pulse representing a quantitized increment having a weight of u and is used as .DELTA.x.sub.i and .DELTA.y.sub.i to another DDA operator. In other words, the data in the .DELTA.z register and .DELTA.z" register are introduced into the adder AD and the unit ALU.sub.1, via the data buses DB.sub.3 and DB.sub.4, respectively, and are used as increments.

When the DDA operates as an integrator, it is represented by a symbolic presentation as shown in FIG. 4 and the integral operation logic is arranged in the following ##EQU4##

When it operates as a servo, it is symbolized as shown in FIG. 5 and the operation logic of y.sub.i is defined by the equation (1) as in the case of the integrator. The operation logic of .DELTA.z.sub.i is independent of .DELTA.x.sub.i and r.sub.i, and defined by ##EQU5## The equation (5) implies that, so long as y.sub.i .noteq.0, .DELTA.z.sub.i pulse is exclusively dependent on the sign of y.sub.i. Such as operation logic is realized in such a manner that, either .DELTA.z.sub.i =+1 or .DELTA.z.sub.i =-1 is determined depending on a state of a sign bit representing a sign of y.sub.i in the Y register and the condition of .DELTA.z.sub.i =0 is determined by detecting a bit state of each digit of the Y register. Therefore, the increment .DELTA.z.sub.i may be formed by the logic circuit LC on the basis of the output signal C.sub.6 of the decoder DC shown in FIG. 1 and the signal C.sub.1 of the sign bit of the Y register latched in the latch LH.sub.1. In other word, when the DDA operates as a servo, it is enough to perform the control as mentioned above by the control unit SPC.

As described above, the DDA commonly uses the adder AD, the arithmetic logic unit ALU.sub.1, and the logic circuit LC, and controls a number of registers under control of the control unit SPC so as to satisfy the objects and the characteristics of the process control. In this way, the DDA digitally realizes the same control function as that of the conventional analog control device. As described above, however, the DDA must extract increments from the whole value of various signals from the process, and this task is troublesome.

The present invention is to provide a DDA capable of providing increments from the whole value. To achieve this function, the DDA is provided with an additional arithmetic logic unit ALU.sub.2 and operates in the following manner.

When the increment request is issued from the control unit SPC, an input signal from the signal point of the process from which the increments are extracted is introduced through the input unit I, for example, I.sub.1, to the Y register Y.sub.1. Then, y.sub.i and r.sub.i-1 are read out from the Y register Y.sub.1 and the R register R.sub.1, respectively, and then are loaded into the latch registers LH.sub.1 and LH.sub.2 to set the A and B inputs of the arithmetic logic unit ALU.sub.1. Simultaneously, r.sub.i-1 is set to the B input of the arithmetic logic unit ALU.sub.2. In the next step, the control unit SPC directs the arithmetic logic unit ALU.sub.1 to caulculate A-B i.e. y.sub.i -r.sub.i-1 and judge whether A=B or A.noteq.B. If A=B, the unit ALU.sub.1 produces a state judge signal C.sub.3 =1. Depending on the states of C.sub.1 and C.sub.3 to C.sub.5, the control unit SPC directs the logic unit LC to judge whether y.sub.i >r.sub.i-1, y.sub.i =r.sub.i-1, or y.sub.i <r.sub.i-1. On the basis of the judgement, the logic circuit LC produces .DELTA.z.sub.i pulse as described in detail later. .DELTA.z.sub.i is set to the A input of the arithmetic logic unit ALU.sub.2 through the shifter SF. In this case, the shifter SF, according to the command from the control unit SPC, shifts the .DELTA.z.sub.i pulse to a digit position in the A input where the .DELTA.z.sub.i pulse has a weight u and then sets it therein. The control unit SPC instructs the arithmetic logic unit ALU.sub.2 to calculate A+B=u+r.sub.i-1 and loads the result of the calculation as r.sub.i into the R register R.sub.1 by way of the selector SL. At this step of the operation, a first cycle of the operation is completed.

The explanation will be given of how .DELTA.z.sub.i is set to the A input of the arithmetic logic unit ALU.sub.2, together with the construction of the logic circuit LC.

For convenience of explanation, the following condition or assumption is set up:

(1) Scope of y and r: -1.ltoreq.y<1, -1.ltoreq.r<1

(2) Expression of y and r: Binary expression of 16 bits, a negative number is represented by a complement of 2 and a sign is given by the most significant bit. Accordingly, the minimum quantitized unit is 2.sup.-15. ##EQU6##

Under these conditions (1) to (7), the logic circuit LC is so designed as to produce an increment .DELTA.z in accordance with the logic of increment output operation defined as follows: ##EQU7## In the above equation, .DELTA.z.sub.i is expressed by the unit u obtained by quantitizing y and r; however, the expression is the same as that in which .DELTA.z.sub.i is expressed in terms of incremental pulses +1, 0, and -1 each having a weight u. According to this logic, when y changes from y.sub.i-1 to y.sub.i, y.sub.i is given by

where .DELTA.y.sub.i is an increment. .DELTA.y.sub.i is expressed in terms of u

where m is an integer. In the operation of the incremental output operation, from the i-th iteration to the (i+m-1)th iteration, a total of m incremental pulses .DELTA.z having a weight u are outputted, while r is corrected by u every iteration to finally be y=r at the (i+m-1)th iteration.

A generation rule of the increment .DELTA.z is shown in Table 1. At No. 1 the states of yi.ltoreq.0 and r.sub.i-1 .ltoreq.0 are established and hence C.sub.1 =0 and C.sub.5 =0 are given in accordance with the above conditions (3) and (6). Due to r.sub.i-1 -y.sub.i, C.sub.3 =0 and C.sub.4 =0 are given in accordance with the conditions (4) and (5). Further, in accordance with the equation (6) of the definition of the incremental output operation logic and the condition (7) of the .DELTA.z.sub.i, .DELTA.z'.sub.i =0 and .DELTA.z".sub.i =1 are held.

Other conditions are obtained in the same manner. Since the arithmetic logic units ALU.sub.1 and ALU.sub.2 calculate the values within the scope defined by the condition (1), when the result of y.sub.i -r.sub.i-1 is below -1 or not less than 1, the sign bit C.sub.4 of the output signal of the arithmetic logic unit ALU.sub.1 does not satisfy the condition (5). This situation correspondings to those in the columns (8) and (9) in Table 1. Let us consider the logic circuit LC to satisfy the generation rule shown in Table 1 even in such a situation. The Karnaugh maps relating to .DELTA.z'.sub.i and .DELTA.z".sub.i prepared on the basis of Table 1 are shown in FIGS. 6 and 7. As known, the Karnaugh map is used to express .DELTA.z'.sub.i and .DELTA.z".sub.i in terms of C.sub.1, C.sub.3, C.sub.4 and C.sub.5 in accordance with the Boolean algebra. In FIG. 6, a cross-point between a column of C.sub.1 C.sub.5 =00 and a row of C.sub.3 C.sub.4 =00 designates a state of .DELTA.z'.sub.i in No. 1 in Table 1. This is correspondingly applied to other situations.

In accordance with the maps of FIGS. 6 and 7, .DELTA.z'.sub.i and .DELTA.z".sub.i are expressed by

In the equation (9), C.sub.3 is a logic NOT of C.sub.3, C.sub.1 C.sub.5 is a logic AND of C.sub.1 and C.sub.5, and C.sub.1 C.sub.5 +C.sub.1 C.sub.5 is a logic OR of C.sub.1 C.sub.5 and C.sub.1 C.sub.5. Accordingly, .DELTA.z'.sub.i is the logic AND of C.sub.3 and C.sub.4 (C.sub.1 C.sub.5 +C.sub.1 C.sub.5)+C.sub.1 C.sub.5. From the equation (10), .DELTA.z".sub.i is equal to C.sub.3. The block diagram 21 shown in FIG. 2 is the expression of the equations (9) and (10) in terms of the logical elements. In FIG. 2, reference numerals 28, 29, 31, 32, 41 and 42 are AND gates: 30 and 33 are OR gates. When the control unit SPC requests the increment output, logical `1` is applied to one of the inputs of each AND gate 41 and 42 to enable the circuit 21 to use the increments .DELTA.z'.sub.i and .DELTA.z".sub.i. The outputs of the logic elements with respect to C.sub.1, C.sub.3, C.sub.4 and C.sub.5 are tabulated in Table 2. Table 2 is so designed that the relations between the respective numbers 1 to 10 and C.sub.1, C.sub.3, C.sub.4 and C.sub.5 are the same as those in Table 1. When both the tables are compared with each other, those tables are coincident with each other with respect to C.sub.1, C.sub.3 , C.sub.4 and C.sub.5, and z'.sub.i and .DELTA.z".sub.i. Therefore, the circuit 21 in FIG. 2 satisfies Table 1. The logic circuit for producing .DELTA.z for effecting the increment outputting is constructed as mentioned above.

How to set the A input of the arithmetic logic unit ALU.sub.2 will now be described. As indicated by the condition (2) the unit u allowable for quantitizing y is 2.sup.-15. Accordingly, u=2.sup.-h may be used as the unit for quantization for an interger h which is 0<h.ltoreq.15. In this case, the equation (8) is rearranged as follows:

In other words, y is inputted into the Y register with the unit of 2.sup.-h. At this time, the shifter SF set the u in the A input of the arithmetic logic unit ALU.sub.2 so that ##EQU8## The hardware of the above relations may be realized in such a way that .DELTA.z'.sub.i is placed to fill the upper bit positions including the h-th bit in the A input, and .DELTA.z".sub.i is placed at the (h+1)th bit position, and 0 is placed to fill the remaining lower bit positions.

The operations of the DDA as an integrator and a servo will be described referring again to FIG. 1, together with the logic circuit for producing the increment.

When the control unit SPC directs the circuit to operate as an integrator, the contents y.sub.i of the Y register and the contents r.sub.i-1 of the R register are read out and the read-out ones are loaded into the latch registers LH.sub.1 and LH.sub.2, and then are set into the A and B inputs of the arithmetic logic unit ALU.sub.1.

After the settings, the increment pulses of independent variable are applied, through the data buses DB.sub.3, DB.sub.4 or DB.sub.6, to the unit ALU.sub.1 where the operation is carried out for A+B or A-B i.e. y.sub.i +r.sub.i-1 or y.sub.i -r.sub.i-1. The result of the operation is stored as r.sub.i into the R register. In the storing into the R register, the sign bit of the (A.+-.B) is ignored and a positive value r.sub.i given by the equation (4) is always loaded into the R register. The overflow of the R register is determined by the logic circuit LC so as to satisfy the equation (4) by using the sign bit C.sub.1 of the y.sub.i, the sign bit C.sub.5 of r.sub.i-1 and the sign bit C.sub.4 of the output signal from the arithmetic logic unit ALU.sub.1 and the increment .DELTA.z is produced on the basis of the determination.

Accordingly, the generation rule of the increment .DELTA.z when the DDA operates as an integrator is shown as in Table 3, and its logic circuit is expressed as shown in the block diagram 22 in FIG. 2.

When the control unit SPC specifies a servo, the incremental pulse is generated only dependent on the sign of the y.sub.i and whether y.sub.i is=0 or not, as described relating to the equation (5). Therefore, the generation rule of increment .DELTA.z is given as shown in Table 4 and its logical circuit 23 is expressed as shown in FIG. 2.

In the block diagram 22, reference numerals 43, 44 and 53, are AND gates. Only when the control unit SPC directs the integrator operation, the SPC applied a signal to one of the inputs of each of the AND gate 43 and 44, so that the circuit 22 operates as an integrator to produce increments.

In the block diagram 23, 56, 45 and 46 designate AND gates. When the control unit SPC directs the circuit 23 to operate as a servo, a signal is applied to one of the input terminals of each AND gate 45 and 46, so that it operates as a servo to produce increments.

As seen from the foregoing, the DDA according to the invention is able to produce increments of a signal representing the whole value of the signal from a process when the DDA is applied to the process control. Therefore, the problem of the increment generation of the conventional device can be solved.

An application of the invention will be described. In the DDA of the invention, the Y register portion, particularly the function thereof, is not modified, so that the inputting of the increment input .DELTA.y.sub.k and the directly inputting of the whole value from exterior are performed in the same way as that of the other DDA devices. Accordingly, the .DELTA.y.sub.k may be defined as shown in FIG. 8. In FIG. 8, an increment of y is expressed by ##EQU9## In other words, the total sum of n input increments is outputted as an output increment. Therefore, the DDA serves as an adder. The conventional adder uses a servo, as shown in FIG. 9. In this case, of the inputs .DELTA.y.sub.k, the n-th input is used to negatively feed back .DELTA.z. The servo continues to output .DELTA.z until the total sum of the increment inputs .DELTA.y.sub.i .about..DELTA.y.sub.n-1 is cancelled by the input .DELTA.y.sub.n. Therefore, when it produces .DELTA.z equal to the total sum of the increment inputs .DELTA.y.sub.1 to .DELTA.y.sub.n-1, y=0 is established and the generation of the increment .DELTA.z stops. However, since the whole value is not accumulated in the Y register, the Y register can not produce a signal corresponding to the whole value to an external device and the maximum number of the input increments to be added is n-1. On the other hand, in the present invention, since the whole value is accumulated in the adder, the R register can produce the whole value to an external device and the maximum number of the input increments to be added is n. Therefore, the device according to the invention may be used not only for inputting a signal of the whole value delivered from the process but also for outputting a control signal of the whole value to the process.