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IFN503: Assessment 2 – Deliverable

Referencing Styles : APA | Pages : 42

Question 2

Tanenbaum (1999) IEEE 754 floating point format is a convention that is followed commonly in computer language for programming and data transmission, this format is of 32 bits, which consist of following bits

Sign bit

Exponent

Mantissa

1 bit (0 for positive and 1 for  negative numbers )

8 bit

23 bits

 

a) Desikan(2001)

+78.875 is given as fixed point decimal number, we need to convert it into

The steps that is followed during conversion of decimal number into IEEE 754 floating point are given below

Step 1:convert decimal number into binary format

Step 2:convert the binary equivalent number into normalized format, to get exponent and mantissa

Step3: the exponent is converted into biased form and converted into binary format, in this example we need to add 27-1 = 127, as 8 bits are taken for the exponent.

Step 4:As mantissa is of 23 bits, take as much zero as needed to have 23 bits

Step 5: take all the 32 bits as given above to get binary value of IEEE 754 floating point number.

Step 6: convert the binary value into hexadecimal value,

So, as per the steps explained above

Step 1: 78.875 = 1001110.11100

Step 2: normalized format: 1.00111011100 *26

Step 3: exponent biased form = 6+127 = 133,in binary notation = 10000101

Step 4: Mantissa   = 00111011100000000000000

Step 5: give binary value of the calculated sign, exponent and mantissa

Sign (1 bit)

Exponent    (8 bits )

Mantissa(23 bits)

0

10000101

00111011100000000000000

Step 6 :

0100

0010

1001

1101

1100

0000

0000

0000

4

2

9

D

C

0

0

0

Using the conversion to convert binary to hexadecimal value, take 4 bits at a time and use the following way

(Bit3)*23+ (bit2)*22+ (bit1)*21+ (bit0)*20

So, the answer is

429DC000

 

 

b) IN this scenario, the hypothetical convention is thought where, the IEEE floating point number consists of

Sign bit

Exponent

Mantissa

1 bit (0 for positive and 1 for  negative numbers )

6 bit

25 bits

+78.875 is the decimal number given which is needed to be converted into this IEEE 754 floating point number.

As explained in the above scenario , the steps are similar , the only difference is the biased exponent value is now different , as the number of bits used for exponent and mantissa is different . the step by step conversion of the number is explained below

Step 1: first we need to convert the decimal number into binary equivalent

78.875 = 1001110.11100

Step 2 : now we need to write the binary equivalent number into normalized format

1.00111011100 *26

Step 3: the biased number for the exponent as , the number of bits are 6, will be 25-1 = 31

So adding the exponent value from the normalized format with 31 we will be biased form of exponent , which will be in decimal format .

6+31 = 37

Step 4: convert the biased decimal from into binary form

37 ==100101

We get the 6 bit exponent in binary form as 100101

Step 5: calculate the mantissa according to the number of bits needed, here 25 bits are given for mantissa, so we will add required number of zero bits.

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