Question

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

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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