Floating Point Exam questions

Q1. A normalised floating point representation uses an 8-bit mantissa and a 4-bit exponent, both stored using 2's Complement format.

In binary write the smallest number that can be represented using this format.

Mantissa-0.1000000

Exponent-1000

B) This is a floating point representation of a number:

1.011000     0010 

Calculate the denary equivalent of the number. 

Answer= -2.5

C) Write the floating point representation of the denary number 12.75

0.1100110     0100

D) Floating point numbers are usually stored in normalised form.

State two advantages of using a normalised representation.

Advantage 1- It is a more precise way of representing values.

Advantage 2- Numbers take up less storage space so more can be stored.

An alternative twos's bit complement format representation is proposed. In the alternative representation 7 bits will be used to store the mantissa and 5 bits will be used to store the exponent. 

Existing representation (8-bit mantissa, 4-bit exponent)

Proposed alternative (7-bit mantissa, 5-bit exponent)
Using a 7-bit mantissa and a 5-bit exponent will allow the decimal point to be moved farther allowing smaller, or larger numbers to be represented. However only having a 7-bit mantissa will restrict you on the accuracy of smaller numbers because there is less bits to work with. This means that some accuracy may be lost.