SU1112356A2 - Fibonacci p-number sequence generator - Google Patents

Abstract

SEQUENCE GENERATOR IR-NUMBER OF FIBONACCI by ap.sp. USSR No. 1091146, on tl and h and y with the fact that, in order to expand the class, solve 1.1x tasks by ensuring {and the possibility of generating sequences for the value of the power of the optimal and modified p-codes, the initial conditions register is entered, the information input which is connected to the input of the initial conditions of the generator, the output of the register of the initial CONDITIONS is connected to the corresponding input of the second adder, and the synchronizing input of the register of the initial conditions to the fourth output of the synchronization unit.

Description

one

The invention relates to automation and computing technology and is intended to generate sequences of power values with arbitrary initial Fibonacci, optimal Fibonacci, optimal, maximum, and modified p-codes, which can be used in modifying these codes and analyzing the Fibonacci, optimal fibonacci and optimal p-codes, given the number 1x in the form of positional codes.

According to the main auth. No. known generator of the sequence of p-numbers Fibonacci, containing 2p + 1 serially connected registers, two adders, the element OR and the synchronization unit, and the input of the initial conditions of the generator of the sequence p-numbers Fibonacci, as well as the outputs of the first and second adders through the element OR connected to the information the input of the first register, the output of which is the output of the Fibonacci sequence of p-numbers and is connected to the first information

the input of the first adder, the output (p + D) of the th register is connected to the second information input of the first adder, the outputs of registers from (p + 0th to 2p + 0th are connected to the corresponding information inputs of the second adder, the first output of the synchronization unit is connected to the synchronization inputs of all registers, the second and third outputs of the synchronization unit are connected to the synchronization inputs of the first and second adders, respectively (fj,

The known generator generates sequences of p-numbers of Fibonacci, as well as sequences of power values of the optimal mbonacci and minimum p-codes, but does not allow obtaining sequences of power values of the optimal and modified p-codes.

The purpose of the invention is to expand the class of tasks to be solved by allowing the generation of sequences of power values of the optimal and modified p-codes.

The goal is achieved by the fact that the generator of the sequence of p-Fibonacci numbers contains

12356S

the initial conditions register, and the formation input of which is connected to the input of the initial conditions of the sequence generator of p-numbers 1 to 5 starters, the output of the initial conditions register is connected to the corresponding input of the second adder, and the sync input of the initial conditions register is connected to the fourth output of the synchronization block.

The drawing shows a functional diagram of the generator sequence of p-numbers Fibonacci.

The generator contains the registers 15 .l.l-l (2p + l) the element OR 2, the adder 3, the synchronization unit 4, the adder 5, the register 6 of the initial conditions.

The values of the power with arbitrary initial conditions of the fibonacci p-code by the digit C are determined by the recurrence relation

About at P40;

25 V

NO with (1)

tfp (n-l) + typ (n-p-l) at.

where Ng is an arbitrary initial condition;

P is the given natural number, the number of the Fibonacci binary p-number system.

Power values with arbitrary initial conditions are simultaneously weights of binary digits of numbers in the Fibonacci binary p-number system. At the same time

p is a generalized Fibonacci number with arbitrary initial conditions.

The power values with arbitrary initial conditions for the optimal Fibonacci p-code are determined by the recurrence relation

O with (|). P (n) |

p + l

  R

Power values with arbitrary initial conditions for the optimal p-code are determined by the recurrence relation o as n 0; Фр (n) p + l (3 S Ф- (п-р-л) - «- Ы) with njO j The proposed generator provides simulation of a sequence of power values with arbitrary initial conditions of Fibonacci-p-code in the first mode of operation, power values with arbitrary initial conditions for optimal Fibonacción r code in the second mode of operation and a sequence of power values with arbitrary initial conditions for the optimal p code in the third mode of operation. In simulating a sequence of power values with arbitrary The basic conditions of the Fibonacci p-code include the registers 1.1-1./P + 1), the element OR 2, the adder 3, and the synchronization block A. The information input of the generator serves to supply the code combination of the initial condition through the OR element to the register 1.1 in the zero clock of the generator operation. Registers 1.11 (p + 1) store the previous (p + 1) power values with arbitrary initial Fibonacci p-code conditions. The formation of each subsequent power value with arbitrary initial conditions is both baked by adder 3 in accordance with the ratio (|). The synchronization unit 4 generates sync pulses controlling the rewriting of the contents of each previous register into each subsequent register, controlling the addition of the contents of the registers I in the adder 3. 1 and 1. (p + |). The OR element is designed to combine the output | of adders 3 and 5. In the simulation of the sequence of power values with arbitrary initial conditions of the optimal Fibonacci p-code, all structural elements of the circuit, except for register 6, participate. In registers 1. 1-1. (2p-t-l) stored power values with arbitrary initial conditions for the optimal Fibonacci p-code for the previous (2p + |) values of the digits of this code. Modeling of subsequent power values is provided by sum64 maters 3 and 5 according to expression (2). The adder 3 forms the p of the first digits, the readings of the power, and the adder 5 forms all subsequent values. Block 4 controls the operation of adders 3 and 5 in such a way that during the rt clock of the generator, starting from the first, the clock pulses the nl adder 3, and in all subsequent clock cycles to the adder 5. In simulating a sequence of power values with arbitrary initial conditions The p-code involves all structural elements with the exception of the hummator. Register 6 serves for storing and issuing (n + l) times the code combination of the initial condition and can be executed as a register with feedback. In registers 1. 1-1. (), The previous (2p + 1) values of the power are stored, and each value is implemented on the adder 5 according to the ratio (3). Block 4 generates sync pulses for registers 1 and 6 and adder 5. i In addition to the specified followers, the proposed generator also makes it possible to simulate power sequences with arbitrary initial conditions for the modified and minimum p-codes. In the binary modified p-cie.the number system for a given integer p. O and any natural D for which there is a whole prsdstag. More than D in the pide, where; dp.l, lZ u all O 6 m n-1. The power values with arbitrary initial conditions Фр (п) are set by the recurrent relation (3) and are formed in the third generator operation mode on the Lth cycle and are generated on the (n + 0 - M cycle. In the binary minimal p-number system for a given integer P O and any natural C and 5 exists as C, CgCVp (S) where,, 1 for all I i S n. The value of power with arbitrary initial conditions is Wp (n + 1), where (p (5) the recurrent is determined and 12356

The ratio (2) is formed by the second generator, the generator's proposed operating mode of the generator allows the generator to be obtained after the (+ 1) -th cycle and is generated on the basis of the value of the optical (and + 2) -th cycle. In this way, along with the post-5s, this extends its functional capabilities generated by known possibilities.