GATE | GATE-CS-2014-(Set-2) | Question 65

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 −14.25. The representation of X in hexadecimal notation is
(A) C1640000H
(B) 416C0000H
(C) 41640000H
(D) C16C0000H


Answer: (A)

Explanation:

Since No is negative S bit will be 1
Convert 14.25 into binary 1110.01
Normalize it : 1.11001 X 2 ^ 3
Biased Exponent (Add 127) : 3 + 127 = 130 (In binary 10000010)
Mantissa : 110010.....0 (Total 23 bits)

Num represented in IEEE 754 single precision format :

1 10000010 11001000000000000000000

In Hex (Group of Four bits) -

1100 0001 0110 0100 0000 0000 0000 0000

Num becomes : C1640000


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