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Binary Expansion
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All rational numbers have repeating binary expansions.  Operations to
access the individual bits of a binary expansion can be obtained by
converting the value to ``RadixExpansion(2)``.  

The expansion (of type BinaryExpansion) of a rational number is
returned by the binary operation. ::

  r := binary(22/7)
      ___
   11.001
                      Type: BinaryExpansion

Arithmetic is exact. ::

  r + binary(6/7)
   100 
                      Type: BinaryExpansion

The period of the expansion can be short or long. ::

  [binary(1/i) for i in 102..106]
      ________
   [0.00000101,
      ___________________________________________________
    0.000000100111110001000101100101111001110010010101001,
         ____________    ____________
    0.000000100111011, 0.000000100111,
       ____________________________________________________
    0.00000010011010100100001110011111011001010110111100011]
                      Type: List BinaryExpansion

or very long. ::

  binary(1/1007)
     ________________________________________________________________________
   0.000000000100000100010100100101111000001111110000101111110010110001111101
     ________________________________________________________________________
     000100111001001100110001100100101010111101101001100000000110000110011110
     ________________________________________________________________________
     111000110100010111101001000111101100001010111011100111010101110011001010
     ________________________________________________________________________
     010111000000011100011110010000001001001001101110010101001110100011011101
     ________________________________________________________________________
     101011100010010000011001011011000000101100101111100010100000101010101101
     ________________________________________________________________________
     011000001101101110100101011111110101110101001100100001010011011000100110
     ____________________________________
     001000100001000011000111010011110001
                      Type: BinaryExpansion

These numbers are bona fide algebraic objects. ::

  p := binary(1/4)*x**2 + binary(2/3)*x + binary(4/9)
               __       ______
   0.01 x^2 +0.10 x + 0.011100
                      Type: Polynomial BinaryExpansion

  q := D(p, x)
             __
   0.1 x + 0.10
                      Type: Polynomial BinaryExpansion

  g := gcd(p, q)
       __
   x+1.01
                      Type: Polynomial BinaryExpansion

See Also:

* ``)help DecimalExpansion``
* ``)help HexadecimalExpansion``
* ``)show BinaryExpansion``