Floating-Point Numbers, Representation, and Manipulation

Question 1

What is the effect on the numbers if the no of bits for the mantissa is increased ?

Answer 1

• The accuracy of a number can be increased by increasing the number of bits used in the mantissa
• But would leave fewer bits for the exponent thus reducing the range of possible values.

Question 2

Overflow

Answer 2

When a calculation produces a number which is larger than the maximum possible values that can be stored.

Question 3

Underflow

Answer 3

Occurs when a binary number is too small it can not be represented accurately in a given floating point system.

Question 4

Why are binary numbers stored in normalised form?

Answer 4

• Normalised numbers are easier to manipulate
• To preserve the maximum possible accuracy in the number.
• To store decimal numbers.