Question

Question 9.1 Half-precision Floating-point Format

Do some research and find out how real (floating point) numbers are represented in Binary.

(a) (10 =6+4 marks) Devise your own 16-bit representation for floating point numbers. Draw a diagram of your representation and explain what the various bits are used for.

Explain in detail:

(i) How many bits are allocated to the mantissa and the exponent, respectively?

(ii) What defines the range and the precision (or accuracy) of the numbers stored in floating point notation?

Answer 1

Half precision floating point numbers use 16 bits for storing the number, that is 2 bytes. In memory out of the reserved bits for Floating point numbers some bits used to store the fractional part called the Mantissa and some bits are used to store the where the fractional point is in the number called the Exponent. The left most bit also called the most swignificant bit is used for sign representaion, which is 0 for positive number and 1 for negative numbers.

a) We can use 16 bit numbers to store floating point number using 10 bits for mantissa, 5 bits exponent and the most significant bit for sign bit as shown in figure below.

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i) For mantissa 10 bits are allocated and for exponent 5 bits allocated. That means we can store number

ii) Floating point numbers the exponent defines the range and the mantissa defines the precision.