9) Assuming that you are required to make an 8 bit floating point representation

Question

9) Assuming that you are required to make an 8 bit floating point representation, with a 3 bit exponent using excess-3 notation and a 4 bit mantissa using normalized notation a) How would the number 0.5 be stored in the byte? b) What is the number that its binary representation is 11101010? 10) Assuming that you are required to make an 8 bit floating point representation, with a 3 bit exponent using excess-3 notation and a 4 bit mantissa using normalized notation. What is smallest positive number that can be stored? What is the smallest number that can be stored?

Explanation / Answer

8 bits floating point representation can be described as:

where:

a7 - Sign bit

a6,a5,a4 - Exponent using excess-3 notation

a3,a2,a1,a0 - Fractional part in normal binary

Solution of 9a) 0.5 to be stored in byte

Step 1: As it is a positive number so sign bit will be 0

Step 2: Convert 0.5 in binary which is 0.1

Step 3: Normalize 0.1 which is 0.1 * 20

Step 4: Convert the exponent to excess-3 , 0 = 011

Step 5: Fill the exponent:

Step: 6 Fill the fraction:

Hence 0.5 can be represented as 00111000

Solution of 9b)

Given:

Step 1: Split the bytes into respective components:

1   110   1010

Step 2: Convert the excess-3 exponent into its decimal equivalent:

110 =3 hence the exponent = 3

Step 3:  Since the exponent is positive, move the radix point three places to the right

-0.1010 * 23

     -101.0

Step 4:  Convert the binary number to decimal

-101.0 = -5.0

Hence number is -5.0

Solution of 10) Smallest positive number that can be stored is 0.0001 and smallest number that can be stored is -0.0001

a7 a6 a5 a4 a3 a2 a1 a0

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