Question

1. Convert the following binary numbers to floating point format. Assume a binary format consisting of a sign bit (+ positive = 0, - negative = 1), a base 2, 8-bit exponent is 130, and 23 bits of mantissa, with the implied binary point to the right of the first bit of the mantissa. Write your final answer out in the IEEE 754 format
   1. +110110.011011₂

Answer 1

110110.011011
=>  1.10110011011 * 2^5

single precision:
--------------------
sign bit is 0(+ve)
exponent bits are (127+5=132) => 10000100
   Divide 132 successively by 2 until the quotient is 0
      > 132/2 = 66, remainder is 0
      > 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 10000100
   So, 132 of decimal is 10000100 in binary
frac/significant bits are 10110011011000000000000

so, 54.421875 in single-precision format is 0 10000100 10110011011000000000000

Answer: 0 10000100 10110011011000000000000