# GATE | GATE 2017 MOCK II | Question 46

The 32 bit floating point representation of (-12) is ___

(A) 11000000010000000000000000000000
(B) 11000001010000000000000000000000
(C) 01000001110000000000000000000000
(D) 11000000110000000000000000000000

Explanation: To convert the floating point into decimal, we have 3 elements in a 32-bit floating point representation:

• Sign (MSB)
• Exponent (8 bits after MSB)
• Mantissa (Remaining 23 bits)

Sign bit is the first bit of the binary representation. ‘1’ implies negative number and ‘0’ implies positive number. Sign bit=1

Exponent is decided by the next 8 bits of binary representation.
Hence the exponent of 2 will be 3. i.e 23=8.
127 is the unique number for 32 bit floating point representation. It is known as bias. It is determined by 2k-1-1 where ‘k’ is the number of bits in exponent field.
Thus bias = 127 for 32 bit. (28-1-1 = 128-1=127)
127+3=130 i.e. 10000010 in binary representation.

Mantissa: 12 in binary = 1100
Move the binary point so that there is only one bit from the left. Adjust the exponent of 2 so that the value does not change. This is normalizing the number.
1.100 x 23
10000000000000000000000
Thus the floating point representation of -12 is
1 10000010 10000000000000000000000

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