If I bind 2 binary vectors using xor, I have as a result the third vector, If I measure the cosine similarity between the first and the third

If I bind 2 binary vectors using xor, I have as a result the third vector, If I measure the cosine similarity between the first and the third, it returns 0.5, which I like, because the third vectors 50% similar to the first. My question: what binding operation should I do if I have real (not binary, ex -0.45) vectors with with negative numbers too if I want the cosine similarity to return 0.5 too?

Another question: If I use circular convolution as binding operation between real valued (ex with values like -0.14) vectors, what similarity measure will give me 0.5 in the example which I gave?