RU2557450C1 - Method of converting binary gray code into binary code - Google Patents

Abstract

FIELD: information technology.

SUBSTANCE: method includes modulo 2 summation of a number in a Gray code with the same number shifted by one (20) bit to the right; modulo 2 summation of the resultant number with the same number shifted by two (21) bits to the right; the subsequent i^th iteration of the summation is carried out with the result shifted by (2i) bits. The operations stop when the next shift results in a zero.

EFFECT: faster operation and higher reliability.

Description

The present invention relates to the field of digital computing and can be used in computing and telemetry systems to perform the operations of translating the numbers represented in the Gray code into binary code and constructing Gray code converters.

From the existing level of technology there is a known method of translating a Gray code into binary, which consists in the following: each bit in a positional binary code is equal to the sum modulo 2 of this and all higher bits in the Gray code. The senior ranks, respectively, coincide (US patent No. 2632058 of March 17, 1953, Knut Donald E. The Art of Programming. Volume 4. Issue 3. Generation of all combinations and partitions // Transl. From English. - M .: I LLC .D. Williams ", 2007. - 208 p., Robert W. Doran. The Gray Code. // Journal of Universal Computer Science. - 2007. - Vol. 13, No. 11. - P. 1573-1597).

The disadvantages of this method are the need to store the original number in the Gray code, accumulate sequentially received bits of the binary code, perform non-cyclic shift operations and add modulo 2, as many times as there are bits in the original number minus one.

The task to which the invention is directed is to increase the speed of the conversion of the Gray code to binary and reduce the necessary resources (elemental and power) of computing or telemetry systems for the specified operation.

This problem is solved due to the fact that the claimed method of converting a binary Gray code to a binary code consists in the fact that the number in the Gray code is added modulo 2 with the same number shifted by one (2 ⁰ ) digit to the right (non-cyclic shift). The resulting number is added modulo 2 with the same number shifted two (2 ¹ ) digits to the right, then the next addition is performed with the result shifted four (2 ² ) digits to the right, etc. Addition operations stop when the next shift to the right leads to zeroing the number. The result of the last addition is the desired binary number.

The number of summations modulo 2 to obtain a binary code is determined by the exponent of the number 2, which, being raised to this degree, will give the number of bits of the converted number.

The technical result provided by the given set of features is to increase the speed and reliability of the devices for converting numbers in the Gray code to binary numbers by reducing the number of necessary addition operations modulo 2. So, for 4-bit numbers, the described procedure must be done twice, for 8 -bit - three times, for 16-bit - four times, etc. Thus, the greater the digit capacity, the more effective the proposed method. Numbers other than standard bits can be supplemented, if necessary, with zeros in the higher digits to the nearest of them. In addition, there is no need for a register for storing the original number in the Gray code and the accumulation of successively obtained bits of the binary code - after the last addition, the number in the binary code is presented in its entirety.

The method of converting numbers in the Gray code to binary numbers is carried out on a device that allows for non-cyclic shift of numbers and summation modulo 2. The method consists in the following:

1) carry out a non-cyclic shift of the original number in the Gray code by one (2 ⁰ ) digit to the right and add modulo 2 with the original number;

2) the resulting resulting number is shifted two (2 ¹ ) digits to the right and added modulo 2 with the result of the previous addition;

3) the result of the previous operation is shifted four (2 ² ) digits to the right and added modulo 2 with the result of the previous addition;

4) the next addition of the result of the previous operation is carried out with the same number shifted by the number of bits determined by the geometric progression 2 ^n-1 , where n is the number of the addition step. Operations are stopped when the next shift results in a nullification of the number. The result of the last addition is the desired binary number.

There is a specific example of the invention:

translating an 8-bit number in Gray code into a binary number in a known manner:

The conversion of an 8-bit number in the Gray code into a binary number by the proposed method:

Translation of a 16-bit number in the Gray code into a binary number by the proposed method:

Thus, the present invention allows to increase the speed and reliability of devices for converting numbers in the Gray code to binary numbers by reducing the number of addition operations required modulo 2. Moreover, the greater the bit depth, the more effective the proposed method compared to the existing one. In addition, there is no need to store the original number in the Gray code and to accumulate successively obtained bits of the binary code.

Claims (1)

A method of converting a binary gray code to binary code, which consists in the fact that the number in the Gray code is added modulo two with the same number shifted by one bit to the right; the number resulting from the addition is added modulo two with the same number shifted two digits to the right; subsequent addition of the result of the previous operation is carried out with the same number shifted to the right by the number of bits determined by the geometric progression 2 ^n-1 , where n is the number of the addition step; the addition operation is terminated when the next shift results in zeroing the number; the result of the last addition is the desired binary number.