Question

Convert -10.5 single-precision floating point binary format.

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Answer 1

Converting 10.5 to binary
   Convert decimal part first, then the fractional part
   > First convert 10 to binary
   Divide 10 successively by 2 until the quotient is 0
      > 10/2 = 5, remainder is 0
      > 5/2 = 2, remainder is 1
      > 2/2 = 1, remainder is 0
      > 1/2 = 0, remainder is 1
   Read remainders from the bottom to top as 1010
   So, 10 of decimal is 1010 in binary
   > Now, Convert 0.5 to binary
      > Multiply 0.5 with 2.     Since 1.0 is >= 1. then add 1 to result
      > This is equal to 1, so, stop calculating
   0.5 of decimal is .1 in binary
   so, 10.5 in binary is 1010.1
-10.5 in simple binary => 1010.1
so, -10.5 in normal binary is 1010.1 => 1.0101 * 2^3

single precision:
--------------------
sign bit is 1(-ve)
exp bits are (127+3=130) => 10000010
   Divide 130 successively by 2 until the quotient is 0
      > 130/2 = 65, remainder is 0
      > 65/2 = 32, remainder is 1
      > 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 10000010
   So, 130 of decimal is 10000010 in binary
frac bits are 01010000000000000000000

so, -10.5 in single-precision format is 1 10000010 01010000000000000000000
in hexadecimal it is 0xC1280000