What the computer really stores for A
The 64 bits of A (sign | exponent | fraction)
What the computer really stores for B
A + B using those exact stored values (perfect maths)
A + B as the computer answers (rounded to a double)
The same answer, as printed (shortest text that reads back the same)
Type any two ordinary decimal numbers. Notice that 0.5 and 0.25 are stored exactly, while most others are not.