Question

Convert the decimal 0.2 to hexadecimal representation using IEEE 754 single precision format

Answer 1

Converting 0.20000000 to binary
      > Multiply 0.20000000 with 2.  Since 0.40000000 is < 1. then add 0 to result
      > Multiply 0.40000000 with 2.  Since 0.80000000 is < 1. then add 0 to result
      > Multiply 0.80000000 with 2.  Since 1.60000000 is >= 1. then add 1 to result
      > Multiply 0.60000000 with 2.  Since 1.20000000 is >= 1. then add 1 to result
      > Multiply 0.20000000 with 2.  Since 0.40000000 is < 1. then add 0 to result
      > Multiply 0.40000000 with 2.  Since 0.80000000 is < 1. then add 0 to result
      > Multiply 0.80000000 with 2.  Since 1.60000000 is >= 1. then add 1 to result
      > Multiply 0.60000000 with 2.  Since 1.20000000 is >= 1. then add 1 to result
      > Multiply 0.20000000 with 2.  Since 0.40000000 is < 1. then add 0 to result
      > Multiply 0.40000000 with 2.  Since 0.80000000 is < 1. then add 0 to result
      > Multiply 0.80000000 with 2.  Since 1.60000000 is >= 1. then add 1 to result
      > Multiply 0.60000000 with 2.  Since 1.20000000 is >= 1. then add 1 to result
      > Multiply 0.20000000 with 2.  Since 0.40000000 is < 1. then add 0 to result
      > Multiply 0.40000000 with 2.  Since 0.80000000 is < 1. then add 0 to result
      > Multiply 0.80000000 with 2.  Since 1.60000000 is >= 1. then add 1 to result
      > Multiply 0.60000000 with 2.  Since 1.20000000 is >= 1. then add 1 to result
      > Multiply 0.20000000 with 2.  Since 0.40000000 is < 1. then add 0 to result
      > Multiply 0.40000000 with 2.  Since 0.80000000 is < 1. then add 0 to result
      > Multiply 0.80000000 with 2.  Since 1.60000000 is >= 1. then add 1 to result
      > Multiply 0.60000000 with 2.  Since 1.20000000 is >= 1. then add 1 to result
      > Multiply 0.20000000 with 2.  Since 0.40000000 is < 1. then add 0 to result
      > Multiply 0.40000000 with 2.  Since 0.80000000 is < 1. then add 0 to result
      > Multiply 0.80000000 with 2.  Since 1.60000000 is >= 1. then add 1 to result
   so, 0.2 in binary is 0.001100110011001100110011
0.2 in simple binary => 0.001100110011001100110011
so, 0.2 in normal binary is 0.001100110011001100110011 => 1.100110011001100110011 * 2^-3

single precision:
--------------------
sign bit is 0(+ve)
exp bits are (127-3=124) => 01111100
   Divide 124 successively by 2 until the quotient is 0
      > 124/2 = 62, remainder is 0
      > 62/2 = 31, remainder is 0
      > 31/2 = 15, remainder is 1
      > 15/2 = 7, remainder is 1
      > 7/2 = 3, remainder is 1
      > 3/2 = 1, remainder is 1
      > 1/2 = 0, remainder is 1
   Read remainders from the bottom to top as 1111100
   So, 124 of decimal is 1111100 in binary
frac bits are 10011001100110011001100

so, 0.2 in single-precision format is 0 01111100 10011001100110011001100
in hexadecimal it is 0x3E4CCCCC