Maybe we should explore a different track. Forget all about the history of computing hardware, and the advantages of one representation over another when designing circuits. In purely mathematical terms, what are the decimal digits of the base-10 number -123 ?
Working backwards: _123 NB. begin -123 NB. notation->operation _1 * 123 NB. definition of - _1 * (1 * 10^2) + (2 * 10^1) + ( 3 * 10^0) NB. positional number notation (_1 * 10^2) + (_2 * 10^1) + (_3 * 10^0) NB. distribution of * over + _1 _2 _3 +/ . * 10^2 1 0 NB. array simplification 10 #. _1 _2 _3 NB. definition of #. Thus, to satisfy the purposes of inversion, we should have: [all examples from here on are purely theoretical, and the results differ in the extant implementations of J]: 10 #.^:_1: _123 _1 _2 _3 And, analogously in base 2: 2 #.^:_1: 2b_101 NB. 2b_101 is J's notation for -101 in base 2 _1 0 _1 #: 2b_101 NB. #: <=> 2&#.^:_1: _1 0 _1 #: _5 NB. _5 <=> 2b_101 (numbers are analytic) _1 0 _1 QED.* -Dan * Backwards compatibility notwithstanding PS: What implications does this have for modulus, as in _10 | 123 ? ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
