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Answer : $-2.0$

Hex : C0000000

Binary value :

1100 0000 0000 0000 0000 0000 0000 0000

Floating point representation :

Sign Bit + Exponent + Mantissa $= 1 + 8 + 23 = 32$ bits

1 10000000 00000000000000000000000

In IEEE-754 Floating point representation 

  • Exponent is biased (real exp+127)
  • Mantissa is normalized ( 1st bit is 1 and is not written)
  • Sign bit 0 : Number is +ve; Sign bit 1 : Number is -ve

now,

Exponent with bias $= 1000\space0000 =128$

Real exponent $\rightarrow E =  128-127 = 1$

Mantissa normalized $= 0000\space0000\space0000\space0000\space0000\space000$

Real mantissa  $\rightarrow M = 1.0000\space0000\space0000\space0000\space0000\space000$

Actual magnitude $=  M\times 2^E =1\times 2^1 = 2$

and sign bit is $1$ so $-2$

 

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