Multiplication of floating point numbers is much easier than addition because you simply multiply the two mantissas and add the exponents. There is no shifting of one of the operands as with addition.

The resulting mantissa can never be equal to or greater than 1 because both the multiplicand and multiplier are less than 1. But with multiplication, the possibility of overflow is much greater because adding two 2-digit numbers could often result in a value greater than 99. But multiplying a large number by a small one poses no special problems and does not necessarily cause the same kind of problem as adding two very different numbers.

Here is an example:

           0.56740 x 1010
     x     0.48293 x 102
     --------------------
           0.2740144 x 1012

Chopped down to 5 bits, this becomes:

          0.27401 x 1012

Determination of the sign of the result is done by simply comparing the signs of the two operands (often called the multiplicand and the multiplier.) Recall that sign-magnitude notation is used. An exclusive OR of the two signs is taken and that is the sign of the result.