SU758171A1 - Digital computer of sine and cosine functions - Google Patents

Description

The invention relates to computing and can be applied in devices for displaying graphic information and in devices of digital radial-circular sweeps 5 for the simultaneous calculation of the sine and cosine functions of the argument given in the form of a unitary code.

The known generator of periodic oscillations, containing a reference voltage source, an integrator, a second reference voltage source, four keys, a functional frequency converter, a reversible counter, a code-voltage converter, two 15 triggers, a filter [ί]. The outputs of the voltage sources through the first and second keys are connected to the input of the integrator. The integrator output is connected to the input of a functional frequency converter, the output of which is through the third and fourth keys, connected to the subtracting and summing inputs of a reversible counter. One output of the counter is connected to the input of the first 25 trigger, and the output of the latter is connected to the control inputs of the first and third keys, the second output of the trigger is connected to the control inputs of the second and fourth keys and to the input vts 30

trigger, and its output is connected to the code-voltage converter. The code-voltage converter output is connected to a filter, and the inputs are connected to the outputs of a reversible counter. In such a device, a sinusoidal voltage is first formed using analog elements, and then this voltage is converted into cosine-varying codes.

However, the low accuracy of the obtained cosine function due to the large number of analog elements, as well as the voltage-code conversion process and the impossibility of obtaining other functions besides cosine, reduces the operational capabilities of the device.

Known sine-cosine functional converter containing reversible counter, decoder, sine code coder, cosine code coder, delay line, reversible counter control trigger, four valve groups, valve switching control trigger, two valves, two triggers, sign trigger, valve, trigger valve control, switch ^ 2]. A reversible counter is connected to a decoder, the outputs of which are connected to a sine code coder and a cosine code coder.

The trigger input of the switch switching control through the delay line is connected to a single output of the reversible counter control trigger. The first inputs of the gates of the group are digitally connected with the first inputs of the gates of the fourth group and with the outputs of the corresponding bits of the sine code encoder. The first inputs of the valves of the second group are digitally connected with the first inputs of the valves of the third group and with the outputs of the corresponding bits of the cosine code encoder. The second inputs of the valves of the first and third groups are connected to a single output of the switch switching control trigger. The second and fourth valve groups are connected to the zero output of the valve switching control trigger. The outputs of the gates of the first and second groups are bitwise connected to each other and the corresponding outputs of the terminals of the sine module code. The outputs of the valves of the third and fourth groups are digitally connected to each other and the corresponding output terminals of the code of the cosine module. The first and second inputs of the reversible counter are connected to the single and zero outputs of the trigger control of the reversible counter, the inputs of which are connected to the outputs of the decoder via a delay line and connected to the input terminal of the device. The counting input of the sign trigger is connected to the zero output of the control trigger of the reversible counter, and the outputs are connected via the triggers to the first inputs of the gates. The second valve terminals are connected via a delay line to the output terminal, and the valve outputs are connected to the output terminals of the sine and cosine signs.

In such a device, the sine and cosine functions are formed simultaneously, and the digital codes of these functions are permanently stored in encoders, where they are selected depending on the change in the function argument or on the state of the reversible counter.

However, the complexity and large amount of equipment due to the high hardware costs attributable to the decoder and the sine and cosine coders, reduce the reliability of the device. In addition, using this device it is impossible to change the amplitude of digital sinusoidal values over large limits, which reduces its functionality.

Closest to the invention is a digital calculator of sine and cosine functions, containing four control units, a clock generator, an argument counter, four groups of AND circuits, a register

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cosine, sine register, two triggers, OR circuit group, sine increment adder, cosine increment adder, correction counter [3].

One of the inputs of the first control unit is connected to the output of the clock generator. The second input of the first control unit is connected to the input of the calculator and the input of the argument counter. The outputs of the first control unit are connected to the first inputs of the four groups of circuits I and to the inputs of the second and third control units, the outputs of which are connected respectively to the inputs of the cosine register and the sine register. The remaining inputs of the cosine register and the sine register are connected to the outputs of the fourth control unit. The inputs of the fourth control unit are connected via two successively connected flip-flops to the output of the argument counter. The second inputs of the first and third groups of circuits AND are connected to the output of the cosine register, and their outputs are connected to the inputs of the first group of OR circuits. The second inputs of the second and fourth groups of AND circuits are connected to the outputs of the sine register, and their outputs are connected to the inputs of the second group of OR circuits. The input of the correction counter is connected to the input of the calculator. The output of the correction counter is connected to the third input of the first control unit. The inputs of the adder of the sine increments are connected to the outputs of the OR circuit of the first group and the output of the first AND circuit of the first group. The output of the adder of the sine increments is connected to the second input of the third control unit. The inputs of the cosine increment adder are connected to the outputs of the OR circuit of the second group and · the output of the first AND circuit of the second group. ' The output of the adder of the cosine increments is connected to the second input of the second control unit.

This device does not allow changing the amplitude of the digital values of sine and cosine, i.e. calculate the function A · 5ΐ η X, A cos X, where A is the amplitude of the digital values of sine and cosine, which limits its functionality.

The aim of the invention is to expand the functionality of the device by calculating the functions A · 5ΐη X, A - Ces X, which allows you to widely change the amplitude of the calculated functions.

This is achieved by the fact that the digital calculator of sine and cosine functions contains the argument counter, the first and second adders, the switch, the sine counter, the cosine counter and the control unit whose outputs are connected to the control inputs of the sine counter and cosine counter whose outputs are the outputs of the calculator the switch output is connected to the input of the second adder, containing decryption5

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Routing zero and a switch, the input of the unitary argument code of the calculator connected to the input of the argument counter and the input of the switch, the control inputs of which are connected to the sign outputs of the first and second adders, and the outputs to the inputs of the sine counter and cosine counter, the inputs of the switch are connected to the outputs of the first adder and the argument counter, the input of the first adder is connected to the sign output of the second adder, which is also connected to the control input of the switch, the input value of the amplitude of the calculator is connected to the inputs of the initial installation of the first and second adders and the cosine counter 15, the output of the argument counter is connected to the input of the zero decoder, the output of which is connected to the input of the control unit and the enable inputs of the recording of the initial installation 20 of the argument counter and the second adder a sign output - the first adder.

The drawing shows the digital calculator of the sine and cosine functions.

It contains the argument counter 1, the first adder 2, the switch 3, the second adder 4, the control unit 5, the sine counter 6, the cosine counter 39 7. The outputs of the control unit 5 are connected respectively to the inputs of the sine counter 6 and the cosine counter 7. The outputs of the sine counter 6 and the cosine counter 7 is connected to 35 output buses of the sine and cosine codes, respectively. The output of the switch 3 is connected to the input of the second adder 4.

The proposed device also contains 40 block 8 allocation zero and switch 9. The input amplitude bus is connected to the first input of the first adder 2 and to the second inputs of the second adder 4 and the cosine counter 7. 45

One of the outputs of the first adder 2 is connected to the first input of the switch 3. The second output of the first adder 2 is connected to the first input of the argument counter 1 and to one of the pedals

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switch 9. The output of the argument counter 1 is connected to the second input of the switch 3 and to the input of the block 8 for the selection of zero. The first output of the zero allocation block 8 is connected to the second input of the argument counter 1 and to one of the inputs of the second adder 4. The second output of the zero allocation block 8 is connected to the input of the control unit 5. The output of the second adder 4 is connected to the second input of the first adder 2, to the second input switch 9 and with the third input of the switch 3. The input bus of the unitary code is connected to the third inputs of the counter of argument 1 and switch 9. The outputs of the switch 9 65

connected to the second input of the sine counter 6 and to the third input of the cosine counter 7.

The counter of argument 1 converts the impulses successively coming along the bus of the unitary code into respectively increasing or decreasing numerical values. Modes of addition or subtraction of pulses are set by the first adder 2.

The first adder 2 is a accumulating adder or reversible counter and performs a subtraction operation for each pulse of the unitary code and the contents of the adder 2 digits "1" or "2" depending on the sign of the result obtained on the second adder 4.

Switch 3 performs the logical function of AND-OR and multiplying by two, and depending on the sign of the result obtained on the second adder 4, connects to the input of the second adder the input of the argument counter 1 or the output of the first adder 2.

The second adder 4 is an accumulator in the acacia adder and performs an algebraic operation of summing the number stored in it with the number present at the output of the switch 3.

 The control unit 5 on the signals coming from the block allocation zero, sets the mode of addition or subtraction of pulses to the sine counter 6 and the cosine counter 7.

The sine counter 6 and the cosine counter '7 are reversible counters and the signals from the switch 9, form at their outputs the numerical values of the functions of the sine and cosine, respectively.

Block 8 selection of zero captures the zero value of the counter of argument 1, then returns to its original state the counter of argument 1 and the second adder 4, and also generates a signal, which changes the mode of operation of counters 6 and 7.

Switch 9, depending on the sign of the results obtained on adders 2 and 4, connects the pulses of the unitary code to the counting inputs of counters 6 and 7.

In the initial state, in the first adder 2, in the second adder 4 and in the cosine counter 7, the code of the amplitude of the function is written. In the counter of argument 1 the number "1" is written. The control unit 1 sets the pulse addition modes for the sine counter 6 and subtraction for the cosine counter 7. Switch 3 connects the output of the argument counter to the input of the second adder 4.

This initial state corresponds to the initial conditions of the functions.

A · 5ϊ π X = 0; A - cos U - A

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The process of forming the numerical values of the sine and cosine functions is performed on the unitary code signals that come to the input of the calculator. Since the second adder 4 is an accumulator of the accumulating type and the output of the counter of argument 1 is connected to its input, the following actions are performed for each pulse of the unitary bank on the second adder 4, and the state of the argument counter for each pulse of the unitary code is increased by one

A - 2 · 1 ·,

A - 2 · (1 + 2);

A - 2 · (1 + 2 +3);

.· · ............... P(

A - 2 (1 + 2 + 3 + ... P.) "A - 2-.Σ".

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If the result, marked after performing each of these actions, is positive, then after the execution of each action, the following operations are performed on the first adder

A - 1;

(A - 1) -. Ί = A - 2;

(A — 2) —1 = A — Sit.d.

If {1, for example, after the action A - 2 · Σι on the second adder 4, a negative result is obtained, then on the first adder instead of the operation A - (AP - 1) - 1 = A - p.

A - (n ₄ - 1) - 2 - A - (n ₊ + 1)

Simultaneously, the switching 3 connects to the input of the second adder 4 the output of the first adder 2, as a result of which 35 the next impulse code (η ₄ + 1) pulse is performed on the second adder 4

if B4 <0. Moreover, the sine counter is 6

works in the mode of addition of impulses,

and the cosine counter 7 is in the subtraction mode, which is set by the control unit 5.

The above algorithm for the operation of the calculator takes place until the first adder 2 has a negative result, which means going through phase ϊ. In this case, the argument counter 1 is switched to the pulse subtraction mode, and the switch 9 connects each pulse of the unitary code to the input of the cosine counter 7, and to the input of the sine counter 6 from the output of switch 9, the unitary code pulses are issued only in the case of a negative result second adder.

If according to the next impulse of the unitary code, the counter of argument 1 assumes the zero state, which means going through the phase ($ + ^), where (K = 0, 1, 2 ...), the block 8 of the zero selection is triggered, according to the signals of which the argument counter 1 and 25 second adder 4 take the initial state, and the control unit 5 changes the operation mode of the counters 6 or 7. For example, when going through the phase, the sine counter 6 switches to the pulse subtraction mode.

Thus, when a pulse of a unitary code arrives at the input of the calculator, which will correspond to the time variation of the function argument Χ (ι) on the sine counter 6 and on the cosine counter 7, we will have periodic functions

Υ (ΐ) = A · s! N X (ί) and Υ (I) = A-cos Χ (ΐ £

The error arising from the calculation of these functions will not exceed the low order unit of the number Υ (ι). However, it creates a technical effect, which consists in expanding the functionality of the device.

Compared with the device-prototype, the proposed calculator allows, at a constant value of the argument X, to calculate the functions А · з! X,

A · co5 X. In this case, the number of pulses of a unitary code must be equal to or proportional to the code of X. With a variable argument of the function (), i.e. when forming codes that vary in time according to the sinusoidal law A · 5Ϊη X (ϊ) and A · cos X (ί),

55 This device allows to change the amplitude of digital sine and cosine function values over a wide range. This circumstance is important when using this calculator for graphic information display devices and radial sweep devices for the image of circles with different radii, since otherwise for 65 performing the multiplication operation A x

(A 2 - ,, 2 -.) + 2- | A - (n ₄ + 1) | = ₄ ⁴⁰

If the result B ₄ thus obtained is positive, then on the first adder 2 the action '

A - (η ₄ + 1) -1 and by impulse (n ₄ + 2) ..

the first adder 4 performs the following operation:

In ₄ - 2 ( _{n <} + 2).

If the resulting B _{4 is} negative, then the following actions are performed:

the first adder 2 - G And - (p, +

+ 1) 3-2 "second adder 4— B ₄ - 2 ·) A -

~ (η ₄ + 1) | - 2 "etc.

Since the bus of the unitary code is connected to the input of the switch 9, these pulses go to counters 6 and 7. In the following order: each impulse of the unitary code arrives at the sine counter 6, the impulse of the unitary code is output to the cosine counter 7 at which the second adder 4 received a negative result, i.e. pulse n ₄ and (η ₄ + 1),

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* 5ίη Χ (ΐ), A · cos Χ (ΐ) will require additional hardware costs, which will increase the amount of graphic information display devices, as well as increase the execution time of the operation A · 5 ϊ η X (g), A - cos X (g) by performing a multiplication operation.

Claims (1)

Claim . The digital calculator of sine and cosine functions containing the argument counter, the first and second adders, the switch, the sine counter, the cosine counter and the control unit whose outputs are connected to the control inputs of the sine and cosine counter whose outputs are the outputs of the calculator, the output of the switch is connected to the input of the second adder, characterized in that, in order to extend the functionality consisting in the possibility of a wide change in the amplitude of the calculated functions, the calculator contains a decoder n the hub and the switch, and the input of the unitary argument code of the calculator is connected to the input of the argument counter and the input of the switch, the control inputs of which are connected with the sign outputs of the first and second adders, and the outputs with the inputs of the sine and cosine counters, the switch inputs are connected to the outputs of the first adder and the instrument counter, the input of the first adder is connected to the sign output of the second adder, which is also connected to the control input of the switch, input of the amplitude value of the calculator for keys к to the inputs of the initial installation of the first and second adders and the cosine counter, the output of the argument counter is connected to the input of the zero decoder, the output of which is connected to the input Lok management and access permitted • 5 Nia recording initial setup argument counter and a second adder, a control input of the counter argument is connected to the output of the first adder landmark. 20