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Consider the single precision (i.e., $32$-bit) floating point representation of numbers in the normalized form where $8$ bits are used for the exponent with the bias of $127.$

  1. What is the binary representation of $-10.4$ in the above form? The steps followed to arrive at the representation must be shown.
  2.  How many different floating point numbers can be represented in the above form, lying strictly between $2^{-18}$ and $2^{-17}$ (i.e., excluding $2^{-18}$ and $\left.2^{-17}\right)?$
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i)

In Single-Precision (32bit notation) :-

   S       E        M

  1bit        8bit           23bit

 

GIVEN      b=127,

              Value: (-10.4)         

              Binary equivalent:  10110.0111 * 10^0 

                                           => 1.01100111 * 10^4

              E=e+b => 4+127 => 131

1 10000011 000...01100111

Hexadecimal Notation:-      (C1800067)


ii)

10K ranged values.

 

pls crct me if Im wrong ;)

 

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