0430. What is the value of adding more bits to the characteristic of the exponent? How can this be illustrated?

The more bits we allocate to the characteristic of the exponent, the more magnitude we will have. In other words, we will be able to represent larger (and smaller) numbers.

Consider the numbers: 1.23, 12300000000000.00, and 0.000000000000123

When we put these numbers in exponential notation we have:

1.23	0.123E1
12300000000000.00	0.123E12
0.000000000000123	0.123E-12

Notice that in exponential form, the mantissa is the same but the value of the characteristic varies (notice also that the characteristic can be either positive or negative). To represent larger (smaller) numbers, we need more bits for the characteristic.