SU1273909A1 - Generator of fibonacci p-numbers sequence - Google Patents

Abstract

The invention relates to the field of automation and computer technology and is intended to generate a series of power values with arbitrary initial Fibonacci optimal, minimum and modified p-codes, as well as the mass of the optimal p-code, specified in the form of positional codes. The purpose of the invention is to expand the class of tasks to be solved due to the possibility of generating sequences of values of the mass of the optimal p-code and the power of the optimal modified p-codes. The generator contains registr. ry of the first group 1.1-1.

Description

112739 The invention relates to automation and computing technology and is intended to generate sequences of power values with arbitrary initial 5 Fibonacci optimal, minimum and modified p-codes, as well as the mass of an optimal p-code, specified in the form of positional codes. The power value with an arbitrary 10 initial Fibonacci p-code conditions of a n size (Fibonacci p-numbers) is determined by the recurrent relation: Opri p O Ng at ChrSp-O + (1).% - ь (p-1) for where N is an arbitrary initial condition; p is a nonnegative integer that specifies the number of the binary p-number system. The power values with an arbitrary initial condition of the optimal Fibonacci p-code and the size of n and the minimum p-code of n-1 are determined by the recurrence relation: with p o at 5 ;; ii4p (n - p - j) with p p with arbitrary initial conditions of optimal and modified p-codes are determined by the recurrence relation: / 0. for n 0% (n) glcp (pj), N,, p „, 0 Another important characteristic of the code is its mass. The values of the mass with arbitrary initial conditions for the optimal p-code, which determine the number of binary units in the set of codewords of power F (n), are given by the recurrence relation: Gopri Sf (n)., (Npj) -t- (4) p (npj) at Table 1 shows the values of the function (4) for p OG / GO and p 1.4 at Table 1 O O 1 2 4 8 13 22 35 54 83 O O 0123 9 15 22 33 O O 0012 6 10 16 О О 0001 The purpose of the invention is to expand the class of tasks to be solved by generating a sequence of mass values of the optimal p-code and the power of the optimal and modified p-codes. The drawing shows the scheme of the proposed generator. The device contains registers of the first group 1.1-1. (2p + 1), element 2, adders 3, 4 and 5, synchronization unit 6, initial conditions register 7, registers of the second group 8.1 - 8. (2p. + 1), information inputs 9 and exits 10 and 11. The generator works as follows. In the initial state, registers 1 .1 - 1. (2p + 1), 8.1 - 8. (2p + 1) and register 6 contain zero codes. In the zero clock cycle, the information input 9 of the generator is given an NJ code, the initial condition, which is fed to the information input of register 1.1 through the OR element 2 and to the information input of register 7 directly. In the mode of simulating a sequence of power values with arbitrary initial Fibonacci p-code conditions, the signal from block 4 output to register t.1 clock input is written to code 1.1 in register 1.1. in the first clock cycle, the contents of register 1.1 under the influence of a signal from the output of the synchronization unit are fed to the information output of the generator 10, to the information input of the register 1.2 and to the first information input of the adder 3, to the second information input of which the contents of the register 1f (p + 1) arrive. According to the signal coming from the same clock cycle from the block code

3

6, the addition of registers 1.1 and 1 received from registers 1.1 and 1. (p + 1) to the adder 3 code combinations of numbers. At the same time, the result of the addition is written to register 1.1 through the element OR 2. Thus, in the first cycle, the first value of the function (1) is obtained. The subsequent values of the sequence of power values with the initial condition of the Fibonacci p-code are formed by repeating the operation of adding the contents of registers 1.1 and 1. (p + 1) and rewriting the contents of 2 registers 1.1 - 1. (p + O. In the first mode of the generator

739094

addition of the contents of the registers 1. (p + 1) - 1. (2p + 1) and the register 7 on the adder 4 and the contents of the registers 1. (p + 1) - 1. (2p + 1), 8. (p + 5 + 1) - 8. (2p + 1) on the adder 5 does not occur, as the synchronization inputs of the adders 4 and 5 do not have the sync pulses of the outputs and the synchronization unit 6.

An example of the functioning of this generator can serve as the formation of a sequence of values of the function (1) with p 2, Ng 2, shown using Table 2.

table 2

In the mode of simulating a sequence of power values with arbitrary initial Fibonacci optimal p-code conditions, the signal from the output of block 6 to the control input of register 1.1 is applied to the register 1.1. In the first clock cycle, the signal from the output of the synchronization unit 6 contains the contents of the register 1.1 enters the information output of the generator 10, the information input of the register 1.2 and the second information input of the adder 3, the first information input of which receives the contents of the 1 (p + 1) -th register. At the same time, the signal from the output of the synchronization unit 6, arriving at the control input of the adder 3, adds the contents of the registers 1.1 and 1. (p + 1). In the same cycle, the result of the addition through the element OR 2 is written to register 1.1. Thus, in the first cycle, the first value of the function (2) is obtained and the first value is formed from the sequence of power values with the initial condition N, the code of which is contained in register 1.1.It will go to the generator output in the second cycle. Subsequent (p-1) values of the F (n) function are simulated in a similar way by repeating the operations of adding the contents of registers 1.1 and 1, (p + 1) and rewriting the contents of registers 1.1-1. (P + 1). Starting with the (p + 1) -th clock of the generator, the formation of clock pulses at the output of the synchronization unit 6 is stopped, and the control signals begin to flow from the output of block 6 to the control input of the adder 4, before (p + 1) -th clock in registers 1 , 1 - 1. (p + 1) the code of the initial state N is written, and in registers 1. (p + 2) - 1. (2р 1) - the zero code. In (p + 1) -th cycle, the signal from the output of block 6 of register 1.1 causes the output information generator 10 p-th power value with the initial condition N, the optimal Fibonacci code and overwriting the contents of the registers 1.1 - 1. (2p + 1 ). At the same time, the information inputs of adder 4 receive the contents of |) register 1. (p + 1) - 1. (2p “1). At a signal from the output of the block, adder 4 performs addition, coming from registers 1. (p + 1) - 1. (2р + i) codes of numbers. The sum code received from the addition of the information output of adder 4 through the element of the IPI 2 is recorded in Tact

2 2 О О О

24

2 2 2 О О

22

22

22

O2

At the output of the generator In the mode of modeling a sequence of power and mass values with arbitrary initial conditions of the optimal p-code, the signal from the synchronization unit 6 is sent to the control input of the register 1.1 by the signal of the synchronization unit 6, and by the signal incoming to the control input of the register from the output of block 6 synchronization10

6

1216

20

6

6 6 4 2

sixteen

.812

four

68

12

66

2

eight

2

46

6

4 6

8 12 16 is in register 1.1. Thus, in the (p + 1) -th cycle, a code (p + 1) -th power value is generated from a sequence of power values with the initial condition N of the optimal Fibonacci p-code, which goes to the output of the generator 10 in the next (p + 2) th tact. Subsequent otherwise, the powers with the initial condition N of the optimal Fibonacci p-code are simulated by repeating the operations of adding the contents of registers 1. (p + 1) to 1. (2p + 1) and overwriting the contents of registers 1.1 - 1. (2p + 1). An example of the functioning of this generator can serve as a simulation of a sequence of functions (2), as shown in Table 3, with p - 2, N 2. Table C, the initial condition code N is entered in register 7. In the first clock cycle, the signal from the output of synchronization unit 6 Register 1.1 is fed to the information output 10 of the generator and the information input of the register 1.2; the contents of registers 1. (p + 1) 1. (2p + 1) goes to the corresponding informational inputs 1 - (p + 1) of the adder 4, to (p + 2) -th

information input which receives the contents of the register 7 on the signal from the output of block 6 synchronization. At the same time, the signal from the output of the synchronization unit 6 arriving at the control input of the adder 4 adds the contents of the registers 1. (p 1) - 1. (2p + 1) and register 7. In the same cycle, the result of adding through the element OR 2 is written to register 1.1. Thus, in the first cycle, the first value of the function (3) is obtained. Subsequent values of function P (n) are simulated in a similar way by repeating the operations of adding the contents of registers 1. (p + f 1) to V, (2p + 1) and register 7 and rewriting the contents of registers 1.1-1. (2p + 1). In the third mode of operation, the addition of the contents of registers 1.1 and 1. (p + 1) does not occur, since the control input of the adder 3 does not contain a signal from the output of the synchronization unit 6.

Consider the operation of the circuit in the simulation of the mass of the optimal p-code with arbitrary initial conditions Bbmie indicated that the contents of registers 1, (p + 1) - 1. (2p + 1) goes to the corresponding information inputs 1 - (p + 1) adder 4 In parallel, the contents of the registers 1. (p + 1) 1t (2p + 1) enters the corresponding inputs 1 - (p + .1) of the adder 5, and on (p + 2) - (2p + 2) the information inputs of which enters the contents of the registers 8. (p + 1) 8, (2p + 1) at the signal from the output of block 6 of synchronization 1, Simultaneously at the signal from the output of block 6 of synchronization coming to the inform Scintillation input adder 5, the contents of registers occurs adding 1 (p + 1) 1, (2p + 1) registers and 8 (p + 1) - 8. The (2p + 1). In the same cycle, the result of the addition is written to register 8.1.

In the first clock cycle, the signal from the output of synchronization unit 6 contains the contents of register 8.1 at the information output 11 of the generator and at the information input of register 8.2, the contents of registers 1, (p + 1) - 1. (2p + + 1) and 8. (p + 1) - 8. (2p + 1) is fed to the corresponding information inputs 1 - (2p + 2) of the adder 5. At the same time, the signal from the output of the synchronization unit 6, which enters the control input of the adder 5, adds the contents of registers 1. (p + 1) - 1. (2p + 1) and 8. (p + 1) - 8. (2p + 1). In the same clock cycle, the result of the addition is written to register 8.1. Thus, in the first cycle, the first value of the function (4) is obtained and the following value is formed from the sequence of mass values of the optimal p-code.

Subsequent values of the sequence of values of the function (4) are formed in a similar way by repeating the operations of adding the contents of registers 1. (p + 1) to 1. (2p + + 1), 8. (p + 1) - 8. (2p + 1) and overwriting the contents of the registers 8,1 8. (2p + 1). At the same time, the first mass value of the optimal p-code is formed at the (p + 1) -th clock of the generator and is generated at the (p + 2) -th clock of the generator.

An example of the functioning of this generator is the generation of sequences of values of functions (3) and (4) with p 2, N 2, as shown in Table 4.

Tables 2-4 contain the contents of the registers at the time of the end of the corresponding clock. . Table 4

O O 2 4 6 10 18 30 4466

O O O 2 4 6 10 18 3044

About About About About .4 6 10 1830

About About About About About 46 1018

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Claims (1)

000 Claims of the Invention A Fibonacci number sequence generator containing a synchronization unit, three adders, an OR element, two groups of (2p + 1) serially connected registers, with the input of the initial conditions of the generator connected to the first input of the OR element, the second and third inputs of which are connected to the outputs of the first and second adders, the output of the OR element is connected to the information input of the first register of the first group, the synchronization inputs of all the registers of both groups are combined and connected to the first The output of the synchronization unit, the second, third and fourth outputs of which are connected to the gating inputs of the first, second and third adders, respectively, the output of the first register of the first group is connected to the output of the generator power values and the first input 6 10 18 30 44 to the formation input of the first adder, the second information input of which is connected to the output of the (p + 1) -th register of the first group, the outputs of the registers from (p + 1) -th to (2p + 1) -th of the first group are connected to information inputs of the second adder, outputs of registers from (p + 1) -th to (2p + + 1) -th second group are connected to the first group of informational inputs of the third adder, the output of the first register of the second group is connected to the output of the generator mass values, the output of the third adder connected to the information input of the first register of the second group, about distinguished by the fact that, in order to expand the class of solved problems by generating the power function of the optimal and modified P-codes and the mass function of the optimal p-code, the initial conditions register is entered into it, and the information input of the initial conditions register is 11127390912 At the input of the task, 5 initial levels are connected to the input of the constant of the second generator, the synchronization input of the ryh adder, the outputs of registers from the initial register of conditions are connected to the (p + 1) -th (2p + 1) -th first group to the p output of the synchronization unit - py are connected to the second rpvnne of information, the output of the register of the initial storage inputs of the third adder.