About these Turing Machine Programs

BinCount:
'BinaryCounter': There are two sections containing 1's and 0s. These are delimited by
tape cells containing 3. The left section will end up with the number of 1's in the
right sectiom, counted in binary notation. The program progessively turns the 1's
in the right section into 2's so that they only get counted once. The left section
counts upwards from 0000000 (0) to 00001101 (13), and there are in fact 13 1's in
the right section.

OnesComp: Forms the 1's complement of the binary number between the 3's. Turns 1's
to 0's and 0's to 1's.

TwosComp: Forms the 2's complement of the binary number between the 3's. First makes
the 1's complement and then adds 1 to form the 2's complement.

Uadd: "Cave Man" addition. Makes 2 "piles" of 1's that are separated into a single
big pile by removing a 1 from the right end of the right-hand pile, and changing the
zero in between into a 1. The resulting pile has the number of 1's as the sum of
the two piles. This sort of primitive "unary" addition does not require counting or
even having a name for numbers. All apologies to cave men.

Usub: "Cave Man" subtraction. Progessively removes 1's from two piles until only
the larger pile remains. Apologies to cave men.

Palindrome: Goes back and forth between the 3's progessively changing 1's and 0's
to 2's, unless it finds a mismatch, at which point it stops. See the notpalindrome
program which has the same code but the tape cells dont' make a palindrome.

busybeaver4: The 4-state busy beaver Turing program. Takes 107 steps and ends up
with 13 1's on the tape that started with all 0's.

busybeaver5c: A candidate for the 5-state busy beaver Turing program. Nobody knows
if this is the actual busy beaver but it is probably close. Takes a whopping
14,876,170 steps to end up with 4098 1's on the tape that started out with all 0's.
You may or may not want to watch this one run to the halt step; it will take
about 10,000 minutes to run at a mean speed of 1500 steps per minute. Time for a
cuppa.


