Question

Write the IEEE floating point representation (single precision) of 3.75 (Show all your steps to get full credit).

Answer 1

Converting 3.75 to binary
   Convert decimal part first, then the fractional part
   > First convert 3 to binary
   Divide 3 successively by 2 until the quotient is 0
      > 3/2 = 1, remainder is 1
      > 1/2 = 0, remainder is 1
   Read remainders from the bottom to top as 11
   So, 3 of decimal is 11 in binary
   > Now, Convert 0.75 to binary
      > Multiply 0.75 with 2.    Since 1.5 is >= 1. then add 1 to result
      > Multiply 0.5 with 2.     Since 1.0 is >= 1. then add 1 to result
      > This is equal to 1, so, stop calculating
   0.75 of decimal is .11 in binary
   so, 3.75 in binary is 11.11
3.75 in simple binary => 11.11
so, 3.75 in normal binary is 11.11 => 1.111 * 2^1

single precision:
--------------------
sign bit is 0(+ve)
exp bits are (127+1=128) => 10000000
   Divide 128 successively by 2 until the quotient is 0
      > 128/2 = 64, remainder is 0
      > 64/2 = 32, remainder is 0
      > 32/2 = 16, remainder is 0
      > 16/2 = 8, remainder is 0
      > 8/2 = 4, remainder is 0
      > 4/2 = 2, remainder is 0
      > 2/2 = 1, remainder is 0
      > 1/2 = 0, remainder is 1
   Read remainders from the bottom to top as 10000000
   So, 128 of decimal is 10000000 in binary
frac bits are 11100000000000000000000

so, 3.75 in single-precision format is 0 10000000 11100000000000000000000
in hexadecimal it is 0x40700000