10.1.3  Examples of representations of normalized floats

• 3.1:
  We have:

  3.1 = 2*(1+ 1 2 + 1 25 + 1 26 + 1 29 + 1 210 +….)   = 2*(1+ 1 2 + ∞ ∑ k=1 ( 1 24*k+1 + 1 24*k+2 ) )

  hence α=1 and m=1/2+∑_k=1^∞(1/2^4*k+1+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)