GATE IT 2008 | Question: 7

Question

The following bit pattern represents a floating point number in IEEE $754$ single precision format

$1 \ 10000011 \ 101000000000000000000000$

The value of the number in decimal form is

• A. $-10$
• B. $-13$
• C. $-26$
• D. None of the above

Answer 1

Sign bit is $1 \implies$ number is negative

Exponent bits- $10000011$

Exponent is added with $127$ bias in IEEE single precision format. So, actual exponent $= 10000011 - 127 = 131 - 127 = 4$

Mantissa bits- $101000000000000000000000$

In IEEE format, an implied $1$ is before mantissa, and hence the actual number is:

$-1.101 \times 2^{4}$

$=-(11010)_{2} = - 26$

http://steve.hollasch.net/cgindex/coding/ieeefloat.html

Correct Answer: $C$

Comments

sir @ Arjun "In IEEE format, an implied 1 is before mantissa" means ??

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-1.101 * 2⁴  is converted in to - (11010)₂ here what we hv done 

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@Arjun sir but here it was not mentioned to take implicit normal form we could have taken explicit normal form ....in these kind of question do we have to always assume implicit normal form

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sry confusion cleared