Since, you have not mentioned the meaning of “negative binary numbers”, so I am considering $2’s$ complement to represent signed numbers or more specifically signed integers.

Suppose, you have to find gray code for $-2.$

Now, there can be many binary 2’s complement representation for $-2,$ for example,

- $110 = -2^2*1 + 2^1*1 + 2^0*0 = -4 +2 + 0 = -2$
- $1110 = -2^3*1 + 2^2*1 + 2^1*1 + 2^0*0 = -8 + 4 +2 + 0 = -2$
- $11110 = -2^4*1 + 2^3*1+2^2*1 + 2^1*1 + 2^0*0 = -16 +8 + 4 +2 + 0 = -2$

and so on.

Now, the corresponding gray-code will be

- $101$ for $110$
- $1001$ for $1110$
- $10001$ for $11110$

and so on.

So, there is no unique gray code for a single negative number. This is the problem with negative numbers but you will not find this problem with non-negative integers.