When talking about Artificial Intelligence, one of the early contributors was Alan Turing (recall the 'Turing Test' for intelligence). This work was late in his career (1950), as the development of modern computers was getting underway and they could begin to experiment.

Interestingly, Alan Turing was also at the forefront in thinking about the formal limits of computing, even before any of these computers existed!

In 1936, he defined an abstract model for computation which we now call the "Turing Machine." We will look carefully at this model and note some interesting facts:

In truth, if you prefer to think of strings of characters over a larger alphabet, that's okay too, so long as the alphabet is finite.

At each step, the following is done:

Shorthand way to describe the program:
(1,0,0,R,2)
(2,0,0,R,3)
(2,1,1,R,2)
(3,0,b,L,5)
(3,1,0,L,4)
(4,0,1,R,2)

Note: If a combination is ever reached for which no rule is given, the machine simply halts.

Let's execute the program on a sample input:

0 1 0 1 1 0     <--  current location is in bold
1               <--  this is the current state

If we can figure out the method to the madness, here's what the program does:
It adds two numbers together, where the two numbers are originally written in unary and delimited by zeros.

e.g.
010110 --> 01110       as 1 + 2 = 3
01110110 --> 0111110   as 3 + 2 = 5

(1,0,0,R,2)  -- move right, past the first 0
(2,0,0,R,3)  -- we've come to the end of a string of 1s
(2,1,1,R,2)  -- move to right past all the 1s
(3,0,b,L,5)  -- we've moved past the last 1 -- done
(3,1,0,L,4)  -- just hit the second string of 1s; shift the 0
(4,0,1,R,2)  -- finish shifting the 0, and go back to state 2