; Unary-to-Binary TM
;-----------------------------------------------------------------
; A Turing machine for converting unary numbers to binary numbers
; by repeatedly calling the BinaryAdd1 machine as a "subroutine"
;
; INPUT: a block of 1's representing a number written in unary
; OUTPUT: a block of 0's and 1's representing the number in binary
;-----------------------------------------------------------------

0  * * * m1    ; Starting state is m1

m1 1 1 L m1    ; Write 0 to the left of the unary string, with an
m1 _ _ L m2    ; intervening space, then move back to the beginning
m2 _ 0 R m3    ; of the unary string and switch to state m4.
m3 _ _ R m4

m4 1 x R m4    ; Replace all unary 1's by x's and move to the
m4 _ _ L m5    ; rightmost x, then switch to state m5.

m5 x _ L m6    ; Erase the rightmost x.

m6 x x L m6    ; Scan leftward over the x's, and then continue
m6 _ _ L m7    ; scanning left to the beginning of the binary
m7 0 0 L m7    ; string of 0's and 1's, stopping on the leftmost
m7 1 1 L m7    ; symbol. Then switch to state s1 to add 1 to
m7 _ _ R s1    ; the binary string.

s1 0 0 R s1    ; Binary Add1 subroutine
s1 1 1 R s1
s1 _ _ L s2
s2 0 1 * s3
s2 1 0 L s2
s2 _ 1 * s3
s3 0 0 L s3
s3 1 1 L s3
s3 _ _ R m8    ; After adding 1, switch to state m8.

m8 0 0 R m8    ; Scan rightward over the binary string of 0's and
m8 1 1 R m8    ; 1's, and then continue scanning rightward to find
m8 _ _ R m9    ; the end of the string of x's.
m9 x x R m9
m9 _ _ L m5    ; Go back to state m5 to continue the loop...

m5 _ _ * halt  ; Halt when no more x's are found in state m5.