0436. Suppose we only allocated 5-bits to the characteristic of the exponent. What level of magnitude can we get and why?

Since 2⁵ = 32, we could associate the 32 values with the characteristic. Since the characteristic of the exponent ban be either negative or non-negative, the range is actually:

-2⁴ to 2⁴ -1 or -16 to 15.

This means that we can move the decimal place 16 positions to the right, or 15 positions to the right. In other words, the we could represent such numbers as:

0.123E15 = 123000000000000

or

0.123E-16 =0.000000000000000123