13.3 - Floating-point Numbers, Representation and Manipulation

Question 1

What are the effects of decreasing the number of bits allocated to manitssa and increasing exponent

Answer 1

• Reduction in percision, as number of bits in mantissa has decreased
• Increase in range, as the number of bits in the exponent has increased

Question 2

Why are floating-point numbers stored in normalized form

Answer 2

• To avoid possibilited that numbers have multiple representations
• Minimizes number of leding 0’s
• Maximizing number of significant bits
• Large/Small numbers can be stored with accuracy

Question 3

State problems that can occur when floating-point number is not normalized

Answer 3

• Loss of percision
• Redundant leading in 0’s in mantissa
• Multiple representations of the same number

Question 4

State why some numbers can lead to rounding errors

Answer 4

• No exact binary conversion for some numbers
• More bits needed to store the number