Your final +1 is not in the expression by OP. You can get it by taking the correction term (x & y & 1) as mentioned in another comment.

Only if you are dealing with unsigned integers.

For signed integers, you need to be careful depending on the language you are using. Most languages provide a signed right shift that doesn’t lose the sign.

Personally, I think shift should always have been a bitwise operator, without sign extension. To me signed right shift feels as sensible as right shifting a floating point number - a shift is bitwise and not an arithmetical operator. But I guess that’s what comes from being brought up on healthy machine code by robots in the steel jungle.

C recommendation: “INT13-C. Use bitwise operators only on unsigned operands” https://wiki.sei.cmu.edu/confluence/plugins/servlet/mobile?c...