Section 21.4: Real Addition (Frame 6)                     [prev][home][next]

Of course, in the setup we described earlier, we were using excess 50 notation, so 1099 isn't even representable. 1050 is actually 100 and 1099 is actually 1049. Thus overflow occurs sooner.

What happens if the exponents are far apart? Then, when the adjustment is made prior to addition, the smaller will get turned into 0. For example:

           0.56740 x 1010
     +     0.48293 x 102
     -------------------

0.48293×102 becomes 0.04829×103, 0.00482×104, 0.00048×105, 0.00004×106 and finally 0.00000×107, but we need to shift until the exponent is 10. Clearly, the first number is so much larger than the second that it is almost like adding 0 to it in real life, and in the world of representable floating point numbers, it is exactly like adding 0 to it.