Floating point numbers

Question 1

What are the two different components of a floating point number, giving any rules where necessary.

Answer 1

Mantissa: value between –1 and 1 in two’s compliment; 2 most significant bits must be different; implied binary point is after the most significant bit

Exponent: integer value in two’s compliment

Question 2

What will happen if you increase the number of bits in the mantissa

Answer 2

Increase the precision of the represented value (allow for smaller fractional values)

Question 3

What will happen if you increase the number of bits in the exponent

Answer 3

Increase the possible range of representable values

Question 4

represent the largest positive value of a normalised floating point number with 10-bit mantissa and 6-bit exponent

Answer 4

Largest positive mantissa, greatest positive exponent:

0111111111 011111

Question 5

represent the smallest positive value of a normalised floating point number with 10-bit mantissa and 6-bit exponent

Answer 5

Smallest positive mantissa, greatest negative exponent:

0100000000 100000

Question 6

What are the two oppositely big and small normalised floating point numbers

Answer 6

Largest negative mantissa, greatest positive exponent:

1000000000 011111

Smallest positive mantissa, greatest negative exponent:

0100000000 100000

Question 7

represent the smallest magnitude negative value of a normalised floating point number using a 10-bit mantissa and 6-bit exponent

Answer 7

Smallest negative mantissa, greatest negative exponent:

1011111111 100000

Question 8

What are two advantages of normalizing numbers

Answer 8

• Increases precision for a given number of bits
• Gives a unique representation of each value