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What is the binary representation of 35.625 assuming IEEE754 double precision?

What is the binary representation of 35.625 assuming IEEE754 double precision?

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Answer #1

binary representation of 35.625:

35 binary is 100011

0.625 binary is 0.101

35.625 = 100011.101

35.625 = 100011.101
Normalizing binary until one non zero is left on the left
100011.101 x 2^0
1000.11101 x 2^2
exponent=2
1000.11101

2+(2^8-1)-1 = (2 +127)
   = 129

129 in binary = 10000001 (exponent)
1000.11101000000000000000
100011101000000000000000 (normalized)

Binary representation of 36.625 in IEEE 754 is
0-10000001 -100011101000000000000000

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