Binary calculation (11 +01010101 )
The two values have differing bit widths which you aren't taking into account.

The value 11 isn't the same as the value 00000011 when 11 comes from a 2-bit system.  Instead, to take into account the two's complement sign you have to sign extend the smaller value into the same space as the larger value.  That means copying the most significant bit into all the "new" bits you add to make it 8-bit.

So, 11 becomes 11111111.  In two's complement, that equates to -1.

01010101 is decimal 85.  85 + -1 is 84.

Alternatively, in binary, 01010101 + 11111111 = 101010100 but since it's 8 bits the top-most bit gets lost, and the result is 01010100 which is 84.