IEEE-754 32-bit floating-point representation

Question

Which of the given number has its IEEE-754 32-bit floating-point representation as $(0 \ 10000000\ 110 0000 0000 0000 0000 0000)$

a) 2.5

b) 3.0

c) 3.5

d) 4.5

Comments

ans 3

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how?

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sorry 3.5

Now done

Answer 1

Sign = 0

Exponent= 10000000

Mantissa = 110 0000 0000 0000 0000 0000

Actual exponent= Exponent- Bias =128-127 =1

Value=(-1)^s *(1.110000.......) * 2¹

      =(-1)⁰ ⨉(1⨉2⁰+ 1⨉2^-1 + 1⨉ 2^-2 + 0⨉2^-3+........)⨉2¹ =3.5

Answer 2

Answer is : 3.5

How to convert 32 bit floating point representation in to decimal ? 

https://youtu.be/TZI6Fd4WmIs

Step 1 : Partition(LtR) the 32 bits in to sign bit(1), exponent bits(8), Mantissa bits (23)

Here in this example - 0 10000000 11000000000000000000000

Step 2 : sign bit is 0. so the decimal value is (-1)⁰. =>    positive.

Step 3 : find p.      Exponent = 127 + p.

here exponent =128

hence p= 1

Step 4 : Write 1.11000000000000000000000                             

now move decimal point 'p' places to the right. hence we get 

11.1000000000000000000000

=>    this is equivalent to 3.5

and that's the answer.