Multiplication

  Multiplication of dyadic digits is simpler than the average operation. Given two dyadics (a,b) and (c,d), we know that a and c are both odd or zero. Hence, if either a or c are zero, the result will be the dyadic digit (0,0). Otherwise, $a \!\cdot\!c$ is odd, so the result is:

$$(a,b) \times (c,d) = (a \!\cdot\!c, b + d)$$

because

$$\llbracket (a \times c, b + d) \rrbracket = \frac{a\!\cdot\!... ... \llbracket (a,b) \rrbracket \times \llbracket (c,d) \rrbracket$$