Examples of representations of normalized floats

• 3.1 :
  We have :
  

  $${\frac{{1}}{{2}}} {\frac{{1}}{{2^5}}} {\frac{{1}}{{2^6}}} {\frac{{1}}{{2^9}}} {\frac{{1}}{{2^{10}}}}$$ 3.1 =

  $${\frac{{1}}{{2}}} \sum_{{k=1}}^{\infty} {\frac{{1}}{{2^{4*k+1}}}} {\frac{{1}}{{2^{4*k+2}}}}$$ =

  
  hence $\alpha$ = 1 and m = ${\frac{{1}}{{2}}}$ + $\sum_{{k=1}}^{\infty}$(${\frac{{1}}{{2^{4*k+1}}}}$ + ${\frac{{1}}{{2^{4*k+2}}}}$). Hence the hexadecimal and binary representation of 3.1 is:

  40 (01000000), 8 (00001000), cc (11001100), cc (11001100), 
  cc (11001100), cc (11001100), cc (11001100), cd (11001101),
  

  the last octet is 1101, the last bit is 1, because the following digit is 1 (upper rounding).
• 3. :
  We have 3 = 2*(1 + 1/2). Hence the hexadecimal and binary representation of 3 is:

  40 (01000000), 8 (00001000), 0 (00000000), 0 (00000000), 
  0 (00000000), 0 (00000000), 0 (00000000), 0 (00000000)