The number –11.375 (decimal) represented as a 32-bit floating-point binary number according to the IEEE 754...

The number –11.375 (decimal) represented as a 32-bit floating-point binary number according to the IEEE 754 standard is

Expert Solution

1 10000010 01101100000000000000000

Explanation:
-------------
-11.375
Converting 11.375 to binary
   Convert decimal part first, then the fractional part
   > First convert 11 to binary
   Divide 11 successively by 2 until the quotient is 0
      > 11/2 = 5, remainder is 1
      > 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 1011
   So, 11 of decimal is 1011 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, 11.375 in binary is 00001011.011
-11.375 in simple binary => 1011.011
so, -11.375 in normal binary is 1011.011 => 1.011011 * 2^3

single precision:
--------------------
sign bit is 1(-ve)
exponent 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/significant bits are 01101100000000000000000

so, -11.375 in single-precision format is 1 10000010 01101100000000000000000

venereology answered 6 months ago

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