But in case if u use explicit then option c

Please explain

Please explain

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+16 votes

The decimal value $0.5$ in IEEE single precision floating point representation has

- fraction bits of $000\dots 000$ and exponent value of $0$
- fraction bits of $000\dots 000$ and exponent value of $−1$
- fraction bits of $100\dots 000$ and exponent value of $0$
- no exact representation

+22 votes

Best answer

(B) is the answer. IEEE 754 representation uses normalized representation when the exponent bits are all non zeroes and hence an implicit '1' is used before the decimal point. So, if mantissa is

0000..0

it would be treated as

1.000..0

and hence the exponent need to be -1 for us to get 0.1 which is the binary representation of 0.5.

More into IEEE floating point representation:

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

0000..0

it would be treated as

1.000..0

and hence the exponent need to be -1 for us to get 0.1 which is the binary representation of 0.5.

More into IEEE floating point representation:

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

+8 votes

In IEEE biasing of exponent is must.

Step 1: decimal 0.5 --> binary 0.1

Step 2: normalize binary 0.1 --> 1.0 * 2^{-1}

Step 3: exponent -1 + 127 = 126 = binary 01111110

Step 4: remove hidden digit from 1.0 --> 0 (1 is implicit in IEEE representation)

Step 5: 0.5 is positive - the sign bit is zero: 0

The next eight bits are the exponent: 01111110

The next 23 bits are the mantissa: 000000000000000000000

Binary result (32 bits): 10111111000000000000000000000000

I think there is something wrong with the question. Arjun Sir, please explain.

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