Question

represent +123.375 in IEEE-754 single precision format.

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Answer 1

Converting 123.375 to binary
   Convert decimal part first, then the fractional part
   > First convert 123 to binary
   Divide 123 successively by 2 until the quotient is 0
      > 123/2 = 61, remainder is 1
      > 61/2 = 30, remainder is 1
      > 30/2 = 15, remainder is 0
      > 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 1111011
   So, 123 of decimal is 1111011 in binary
   > Now, Convert 0.37500000 to binary
      > Multiply 0.37500000 with 2.  Since 0.75000000 is < 1. then add 0 to result
      > Multiply 0.75000000 with 2.  Since 1.50000000 is >= 1. then add 1 to result
      > Multiply 0.50000000 with 2.  Since 1.00000000 is >= 1. then add 1 to result
      > This is equal to 1, so, stop calculating
   0.375 of decimal is .011 in binary
   so, 123.375 in binary is 1111011.011
123.375 in simple binary => 1111011.011
so, 123.375 in normal binary is 1111011.011 => 1.111011011 * 2^6

single precision:
--------------------
sign bit is 0(+ve)
exp bits are (127+6=133) => 10000101
   Divide 133 successively by 2 until the quotient is 0
      > 133/2 = 66, remainder is 1
      > 66/2 = 33, remainder is 0
      > 33/2 = 16, remainder is 1
      > 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 10000101
   So, 133 of decimal is 10000101 in binary
frac bits are 11101101100000000000000

so, 123.375 in single-precision format is 0 10000101 11101101100000000000000
in hexadecimal it is 0x42F6C000