how to convert a negative binary number to its gray code

Question

I have negative binary number which has a sign bit and want to write a program to get its gray code. However, I can only find the solution for positive number. So here I am asking this question. Thanks.

Answer 1

Gray code can only be calculated for non-negative numbers, using the following method:

int gray_encode(int n) {
    return n ^ (n >> 1);
}

The same method won't work for negative numbers because of Two's complement representation of binary numbers.

Answer 2

It is possible to convert a signed integer to Gray code if the target bit width is known:

int gray_encode(int n) {
    return n ^ (n >> 1);
}

int gray_encode_signed(int n, int width_bits) {
    int all_ones = (1 << width_bits) - 1;
    return (n >= 0 ? gray_encode(n) : gray_encode(abs(n)) + all_ones);
}

For example, this is 4 bits Gray code for values from -7 to 7:

decimal   4bit gray code
     -7    1011
     -6    1100
     -5    1110
     -4    1101
     -3    1001
     -2    1010
     -1    1000
      0    0000
      1    0001
      2    0011
      3    0010
      4    0110
      5    0111
      6    0101
      7    0100