ISRO-DEC2017-75

Question

In $\text{IEEE}$ floating point representation, the hexadecimal number $\text{0xC0000000}$ corresponds to

• A. $-3.0$
• B. $-1.0$
• C. $-4.0$
• D. $-2.0$

Comments

-2.0

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can u explain please?

Answer 1

• Sign bit S = 1 ⇒ Negative number
• Exponent E = 1000 0000  = 128 (in normalized form)
• Original Exponent = 128-127 =1
• Fraction is 1.0 B (with an implicit leading 1) = 1
• The number is -1 × 2^1 = -2 

Answer is D

Answer 2

Input : 0xC0000000 = 1100 0000 0000 0000 0000 0000 0000 0000

32 bit representation  = 1(sign)     100 0000 0(expoanat)      000 0000 0000 0000 0000 0000 (mantissa)

so number is: where bais = 2^8-1 -1 = 127

= (-1)^s $\times$1.M 2^{biased expoanant - bais}

= (-1)¹ $\times$1.0 2^{128 - 127}

= -1.0 $\times$  2

= -2.0