“Convert the decimal number 10/32 to the 32-bit IEEE 754 floating point and express your answer in hexadecimal.”
I understand how to convert a decimal number to IEE 754. But I am confused on how to answer this—it only gives me a quotient? I am not allowed to use a calculator, so I am unsure how to work this out. Should I convert them both to binary first and divide them?
I see it like this:
10/32 = // input
10/2^5 = // convert division by power of 2 to bitshift
1010b >> 5 =
.01010b // fractional result
--^-------------------------------------------------------------
|
first nonzero bit is the exponent position and start of mantissa
----------------------------------------------------------------
man = (1)010b // first one is implicit
exp = -2 + 127 = 125 // position from decimal point + bias
sign = 0 // non negative
----------------------------------------------------------------
0 01111101 01000000000000000000000 b
^ ^ ^
| | mantissa + zero padding
| exp
sign
----------------------------------------------------------------
0011 1110 1010 0000 0000 0000 0000 0000 b
3 E A 0 0 0 0 0 h
----------------------------------------------------------------
3EA00000h
Yes the answer of Eric Postpischil is the same approach (+1 btw) but I didn't like the formating as it was not clear from a first look what to do without proper reading the text.