How to perform unassigned sum with short variable with out converting in to integer in java

Java doesn't have an addition operator for short values. If you look at JLS 15.18.2 (Additive Operators (+ and -) for Numeric Types) you'll see that one of the first things that happens is:

Binary numeric promotion is performed on the operands (§5.6.2).

That will always convert short values into int, float, long or double values, depending on the other operand.

Basically, to perform 16-bit addition, you let the compiler convert both operands into 32 bits, do the addition, and then cast back:

(short) (a + b)

... being aware that this may lose information due to overflow when casting.