Integer number
Numeral system
The original value of the binary
From the source to the gray code(binary)
result binary
From gray's code to the original (binary)
result binary
The original value in the specified calculus
From the source to the gray code(set calculus)
result binary
From gray's code to the original (given calculus)
result binary

 

The calculator allows you to convert a given number into gray's code, and do automatic reverse conversion.

The property of these codes is that when a number is changed to an adjacent one, the binary bits composing it changed only in one position.

Dec     Bin     Gray
0       0000   0000
1       0001   0001
2       0010   0011
3       0011   0010
4       0100   0110
5       0101   0111
6       0110   0101
7       0111   0100
8       1000   1100
9       1001   1101
10     1010   1111
11     1011   1110
12     1100   1010
13     1101   1011
14     1110   1001
15     1111   1000 

 

As you can see, the neighboring numbers represented by the gray code change only one, and only one bit.

Where can this be applied? For example, in biology, when the genome chain can be encoded by the gray code, and then the minimum mutation in one position, will mean a change in one position of the gray code, and therefore the number in the decimal system will differ only by one.

Gray's code can be created only for binary representations of numbers, in other number systems, codes like gray's code can not be created.

But! No one forbids us to take any integer in any number system, translate it into binary form, apply gray's code and return it back to the original number system.

Our calculator does that. It produces the result in both the original number system and binary. In my opinion it is very convenient.

For example, taking our decimal system and then the number 343 in gray's code looks like 508. With one click, the number 343 was converted to binary, gray's code was extracted from it, and the number was converted to decimal again.

How to convert hexadecimal number gray code and back again, better than Wikipedia is not written. Algorithms are also taken from there.

Some examples of transformations

Input

1010100101000010100101010101010101

Answer:

The original value of the binary
From the source to the gray code(binary)
result binary
From gray's code to the original (binary)
result binary
The original value in the specified calculus
From the source to the gray code(set calculus)
result binary
From gray's code to the original (given calculus)
result binary

Example2:

Integer number
Numeral system
8
 
 
The original value of the binary
From the source to the gray code(binary)
result binary
From gray's code to the original (binary)
result binary
The original value in the specified calculus
From the source to the gray code(set calculus)
result binary
From gray's code to the original (given calculus)
result binary
Copyright © 2020 AbakBot-online calculators. All Right Reserved. Author by Dmitry Varlamov