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World's first binary computer? Chessboard 64-square uses Rook and Bishop
moves. [Addition algorithm: depict each number to add across a rank by
'R' counters, then use Rook moves to slide all the representations to
Rank 1; right to left, replace any and all 'doubles' by one to left, 
  ___ ___ ___ ___ ___ ___ ___    continuing until each first-rank square
  ___ ___ ___ ___ ___ ___ ___    is binary 1 or 0, where a 'Rook' is 
  ___ ___ ___ ___ ___ ___ ___    '1']  Bishop-like multiplication to
  ___ ___ ___ ___ ___ ___ ___    left shows chess-computer-abacus' 19x13
  ___ ___ ___b___ ___ ___b___b 1  operation (differing procedure than for
  ___ ___ ___b___ ___ ___b___b 1  Addition).  After placement, Bishop-
  ___ ___ ___ ___ ___ ___ ___  0  counters are to move diagonally left
  ___ ___ ___B___ ___ ___B___B 1  downward. Moves become b d4-a1,
128  64  32  16  8   4   2   1     b d3-b1, b g4-d1, b g3-e1, 
 a   b   c   d   e   f   g   h     b h4-e1 and b h3-f1, making first Rank now:   B___B___ ___BB__BB___B___B___B  and again replacing the 'doubles' with  just one to each pair's adjacent left:
           B___B___B___B___ ___B___B___B  =   11110111  = 247(base 10)
          --Method of John Napier in 1617 'Rabdologia', including also
Subtraction, Division and Extracting Square Roots on chessboard, improves
Middle Age calculating methods: 'bank' deriving from German counting
board, Rechenbank.  Scientific American 1985