Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!watmath!clyde!burl!we13!ihnp4!cbosgd!cbscc!cbneb!cbnap!tjl From: tjl@cbnap.UUCP Newsgroups: net.puzzle Subject: Another sequence (possible correction) ** SOLUTION ** Message-ID: <178@cbnap.UUCP> Date: Mon, 27-Feb-84 09:08:10 EST Article-I.D.: cbnap.178 Posted: Mon Feb 27 09:08:10 1984 Date-Received: Tue, 28-Feb-84 13:31:56 EST Lines: 64 I haven't seen a solution to the puzzle as origionally posted, so I'm including the solution to the puzzle in this form... 1, 110, 111, 100, 101, 11010, 11011, 11000, 11001, ? the sequence continues... 11110, 11111, 11100, 11101, 10010, 10011, 10000, ... SOLUTION . . . . . . . . . . . . . . . The sequence is the counting numbers in negabinary (radix -2). If you've never tried a negative radix before, it is worth exploring a little. For example, no unary signs are needed to indicate negative or positive numbers. The addition table is... 0 1 |---------| 0 | 0 | 1 | |---------| 1 | 1 | 110 | |---------| Try adding one and negative one. (Note what happens to carries.) 11 + 1 --- 0 It should be possible to design a computer to use negabinary arithmetic instead of one or two's complement arithmetic. (There's a good master's thesis for some EE.) Using a decimal point for rational values works fine (as would some sort of floating point standard). QUESTION: What happens to logs in negabinary? By the way, if there is a solution to the problem as origionally posted (fifth element was 1001 instead of 101), I'd like to see the solution.