GATE | GATE CS Mock 2018 | Set 2 | Question 29

The value of a float type variable is represented using the single-precision 32-bit floating point format IEEE-754 standard that uses 1 bit for sign, 8 bits for biased exponent and 23 bits for mantissa. A float type variable X is assigned the decimal value of −25.75. The representation of X in hexadecimal notation is
(A) 61CD0000
(B) C1640000
(C) C1CD0000
(D) C1CE0000


Answer: (D)

Explanation:

Since number is negative S bit will be 1
Convert -25.75 into binary 11001.11
Normalize it : 1.100111 X 2 ^ 4
Biased Exponent (Add 127) : 4 + 127 = 131 (In binary 10000011)
Mantissa : 100111.....0 (Total 23 bits)

Num represented in IEEE 754 single precision format :

1 10000011 10011100000000000000000

In Hex (Group of Four bits) -

1100 0001 1100 1110 0000 0000 0000 0000

Num becomes : C1CE0000

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