Question

Determine the single precision 32-bit representation of:

2^-30

Please show all steps and all work, I'm having trouble figuring out how to do this

Answer 1

normalized form of 2^-30 is 1.0 * 2^-30
(by just multiplying 1 with 2^-30)

single precision:
--------------------
sign bit is 0(+ve)                      ->  because this is positive. 0 is used for positive.
exp bits are (127-30=97) => 01100001    ->  power of 2 is -30, bias is always 127. exponent value bias+power = 127+30 = 97. In binary 97 is 01100001
frac bits are 00000000000000000000000   ->  because all are zeros after dot(.) in 1.0

so, 2^-30 in single-precision format is 0 01100001 00000000000000000000000
in hexadecimal it is 0x30800000