Floating point numbers - accuracy v range

Imagine that you have ten boxes in which to represent a denary number in scientific notation. You have to decide how many places to allow for the sign, how many for the mantissa and how many for the exponent. The choices that you make will affect the range and accuracy of the numbers you can hold. Let's look at some examples to see what we mean. Let us invent a system for storing the digits of a scientific number. Suppose we decide on the following system, where each box can hold one number:


What is the biggest number it can hold?


What happens if you want to represent a really massive exponent, e.g. 345 in the number 0.45 x 10345?

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