Floating point

Question

Consider the following bit pattern represents the floating point number in IEEE 754 single precision format:

1 10000111 11100000000000000000000

Which of the following represents the decimal value of above floating number?

A) -192

B) -320

C) -384

D) -448

Comments

@Shaik Masthan 
Bhai My bad😅, will make sure to make it clear for further questions.

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ok, but please type the questions instead of screenshots otherwise finding duplicates going to be tough !

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Consider the following IEEE single precision floating point number shown below:
0 1 0 0 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
The octal equivalent of above number is

640

Answer 1

In $\text{IEEE-754}$ single precision formate ($32$ bit)  binary number is represented as:

$\text{S(1 bit) E(8 bit) M(23 bits)}$,

with implicit normalization and exponent is represented with $\text{Excess-127}$ code.

So here,

• Sign bit= $1$ $\Rightarrow$ number is negative.
• Exponent bit= $10000111=135 \Rightarrow 135-127=8$
• Mantissa bit= $11100000000000000000000 = 1.111 \rightarrow(\text{implicit normalized form})$

$\therefore V= (-1)^S*1.M*\text{Base}^{E-127}$

$\Rightarrow V=(-1)^1*1.111*\text{2}^{135-127}$

$\Rightarrow V= -1*(1.111)_2*\text{2}^8$

$\because (1.111)_2=(1.875)_{10}$

$\therefore V= -1* 1.875*256= -480$

So correct decimal value is $-480.$

Answer 2

Sign bit	Exponent (Biased)	Mantissa (Normalized)
1	10000111	11100000000000000000000

 

Biased Exponent = $2^{n-1}-1$ = $2^{8-1}-1$ = 127

Number = $-1^{sign bit}$*1.M* $2^{Exponent-Biased Exponent}$

=> -1*1.11100000000000000000000*$2^{135-127}$

=>-1.11100000000000000000000*$2^8$

=>-111100000.000000000000000

=>(-480)$_{10}$