SU1104493A1 - Generator of (n,p) number sequences with variable initial conditions - Google Patents

Abstract

The SEQUENCE SEQUENCE (R, P) is NUMBER with VARIOUS INITIAL CONDITIONS, containing p + 1 serially connected registers from the first to (p + 1) -th, the adder and the synchronization unit, the first information input and the output of the first register being the initial input conditions and the output of the generator sequences (r, p) numbers, the output of the adder is connected to the second information input of the first register, the output of which is connected to the first information input of the adder, the first and second outputs of the synchronization unit connected to the synchronization inputs of the registers and the adder, respectively, characterized in that, in order to expand the class of solved tasks by providing the possibility of generating numbers with the parameter r 1, it contains in addition the r-1 successors about the connected registers from (p + 2) to (g + p) -th and switch, with the output of the (p + 1) -th register connected to the information input (p + 2) of the th register, the outputs of registers from the second to (d-1) -th and output (g + About-th register connected to the corresponding (L ch ush informational inputs of the switch that controls the input Which is the input for setting the operation mode of the sequence generator (r, p) -numbers, the synchronizing input of the switch is connected to the third output of the synchronization block, the output of the switch is connected to the second information input of the adder. 4; i 4 CO 00

Description

The invention relates to automation and computing and can be used to obtain generalized sequences of (t, p) numbers with arbitrary initial conditions. A generator of sequences of generalized (r, p) numbers, containing registers, c / curtains, control and normalization blocks, is known. . This generator is intended to form sequences of generalized () numbers at r 2 G13. However, this generator does not allow to obtain a sequence of Fibonacci numbers. The closest technical solution to the invention is a generator of sequences of (r, p) numbers with arbitrary initial conditions containing p + 1 serially connected registers, an adder and a synchronization unit, the outputs of the first and (p + 1) -th registers being connected to the inputs of the adder, the output of the adder is connected to the input of the first register, the output of the first register is the output of the sequence generator 2. The known generator generates sequences with the parameter g (Fibonacci numbers), but does not allow obtaining sequences with the purpose of the invention. It is an extension of the class of problems to be solved by providing the possibility of generating numbers with the parameter. The goal is achieved by the fact that the generator of sequences of (r, p) -numbers with arbitrary initial conditions, containing p + 1 serially connected registers from the first to (p + 1) -s, the adder and the synchronization unit, the first information input and the output of the first register is, respectively, the input of the initial conditions and the output of the sequence generator (r, p) of numbers, the output of the adder is connected to the second information input of the first register, the output of which is connected to the first information input of the adder, the first and the second synchronization block codes are connected to the synchronizing inputs of all the registers and the adder, respectively, additionally contains d-1 serially connected: registers with (p + 2) -th to () -th and switch, and the output (P + O-GO register connected to the information input of the (p + 2) -th register, the outputs of the registers from the second to () -th and output of the (r + p) -th register are connected to the corresponding information inputs of the switch, the control input of which is the input of the Operation mode setting sequence generator (r, p) numbers, sync yuschy switch input is connected to the third output of the synchronization unit, the switch output is connected to the second data input of the adder. The drawing shows a functional diagram of a generator of sequences of (r, p) -numbers with arbitrary initial conditions for the case,. The circuit contains the synchronization unit 1, registers 2.1-2.4, the switch 3, the adder 4, the input 5 of the initial conditions, the input 6 of the setting of the operating mode, the output 7 of the generator. The generator generates the sequences defined by the following recurrent relation: f О as i 0; , в, - {q when i - 0; (one) . - -r + ... + / i;..+/i;.,, p with ,, 3, .., where Р, - (г, р) is a number, QP is an arbitrary initial condition, г, p - parameters of sequences. As can be seen from (1), when we have a row of Fibonacci numbers, when and, 2,3 ... we get a sequence of generalized Fibonacci numbers, when we get a known classical binary sequence. The generator can operate in two modes: the formation of a sequence of generalized (r, p) -numbers; forming a sequence of Generalized p-numbers-Fibonacci. The mode of operation is set to input 6. In the initial state, all registers are set to zero. On entry 5 initial conditions in the register 2.1. q value is entered. The formation of the next number in the sequence takes place within one cycle. In the first cycle of each cycle, the synchronizing signals from block 1 on the synchronizing - inputs of the adder 4 and switch 3 provide the supply of the number from the first register 2.1 to the first input of the adder and from

3. 1

(r + p) th register 2.4 through switch 3 to the second information input of the adder, in which the sum of these numbers is formed. In the following r-1 cycles when operating in the first mode, the outputs of the registers (r-l) -ro through the second (2.3-2.2) are sequentially connected to the second input of the adder and their contents are added to the contents of the adder. When operating in the second mode, the outputs of the registers from (r-1) -th to the second are not connected to the input of the adder. As a result, in the rth clock cycle on the adder 4, the next number in the sequence is formed according to expression (1).

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At the (r + 1) -th and last cycle of the cycle, the contents of adder 4 are shifted to the first register 2.1, the contents of the first register 2.1 to the second register 2.2, and so on. At generator output 7, the next sequence number appears.

Thus, the proposed generator along with the sequence

generalized Fibonacci numbers generated by a known generator allows to obtain and sequences of generalized (r, p) -numbers with

extends its functionality.

five

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Claims (1)

SEQUENCE GENERATOR (R, P) -NUMBER WITH ARBITRARY INITIAL CONDITIONS, containing p + 1 series-connected registers from the first to (p + 1) -th, adder and synchronization block, and the first information input and the output of the first register are respectively the input of the initial conditions and the output of the sequence generator (g, p) ^_ numbers, the output of the adder is connected to the second information input of the first register, the output of which is connected to the first information input of the adder, the first and second outputs of the synchronization unit are connected are geared towards the synchronizing inputs of the registers and the adder, respectively, characterized in that, in order to expand the class of problems to be solved by providing the possibility of generating numbers with the parameter r? 1, it additionally contains r-1 registers connected in series from (p + 2) -th to (r + p) -th and a switch, and the output of (p + 1) -th register is connected to the information input of (p + 2) th of the register, the outputs of the registers from the second to the (r-1) -th and the output of the (r + 1) -th © register are connected to the corresponding information inputs of the switch, the control input of which is the input of the job of the operating mode of the sequence generator (g, p) -number) , the synchronizing input of the switch is connected to the third output of the synchronization unit, the output of the switch is connected to the second nformatsionnomu input adder. 1104493 2