Question

Convert 1234.125 into 32-bit IEEE floating-point format What is the decimal equivalent of the 32-bit IEEE floating-point vahue CC4C000016 Draw a truth table to represent the intermediate vahues and output of the circuit below Also, write down the Boolean expressions for intermediate and final outputs А В D ш.

Answer 1

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Converting 1234.125 to binary
   Convert decimal part first, then the fractional part
   > First convert 1234 to binary
   Divide 1234 successively by 2 until the quotient is 0
      > 1234/2 = 617, remainder is 0
      > 617/2 = 308, remainder is 1
      > 308/2 = 154, remainder is 0
      > 154/2 = 77, remainder is 0
      > 77/2 = 38, remainder is 1
      > 38/2 = 19, remainder is 0
      > 19/2 = 9, remainder is 1
      > 9/2 = 4, remainder is 1
      > 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 10011010010
   So, 1234 of decimal is 10011010010 in binary
   > Now, Convert 0.125 to binary
      > Multiply 0.125 with 2.   Since 0.25 is < 1. then add 0 to result
      > Multiply 0.25 with 2.    Since 0.5 is < 1. then add 0 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
   0.125 of decimal is .001 in binary
   so, 1234.125 in binary is 10011010010.001
1234.125 in simple binary => 10011010010.001
so, 1234.125 in normal binary is 10011010010.001 => 1.0011010010001 * 2^10

single precision:
--------------------
sign bit is 0(+ve)
exp bits are (127+10=137) => 10001001
   Divide 137 successively by 2 until the quotient is 0
      > 137/2 = 68, remainder is 1
      > 68/2 = 34, remainder is 0
      > 34/2 = 17, remainder is 0
      > 17/2 = 8, remainder is 1
      > 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 10001001
   So, 137 of decimal is 10001001 in binary
frac bits are 00110100100010000000000

so, 1234.125 in single-precision format is 0 10001001 00110100100010000000000
in hexadecimal it is 0x449A4400

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