This is the fourth part of the Turing Machine series. For your convenience you can find other parts in the table of contents in Part 1 – Addition

Today we subtract two numbers. This is very similar to addition so should be pretty readable.

States:

q0 - looking for the beginning, no borrow q1 - looking for the beginning, with borrow q2 - looking for the first number digit, no borrow q3 - looking for the first number digit, with borrow q4 - 0 from the first digit, looking for boundary, no borrow q5 - 1 from the first digit, looking for boundary, no borrow q6 - 1 from the first digit, looking for boundary, with borrow q7 - 0 from the first digit, looking for the second number digit, no borrow q8 - 1 from the first digit, looking for the second number digit, no borrow q9 - 1 from the first digit, looking for the second number digit, with borrow q10 - 0 in the difference, looking for the end of the second number, no borrow q11 - 1 in the difference, looking for the end of the second number, no borrow q12 - 1 in the difference, looking for the end of the second number, with borrow q13 - 0 in the difference, looking for the end of the second number, with borrow q14 - 0 in the difference, looking for a place to write, no borrow q15 - 1 in the difference, looking for a place to write, no borrow q16 - 1 in the difference, looking for a place to write, with borrow q17 - 0 in the difference, looking for a place to write, with borrow

The input looks like this:

$aaaa%bbb^

Transition table:

0,q0,0,q0,L 1,q0,1,q0,L ^,q0,^,q0,L %,q0,%,q0,L $,q0,$,q2,R 0,q1,0,q1,L 1,q1,1,q1,L ^,q1,^,q1,L %,q1,%,q1,L $,q1,$,q3,R 0,q2,$,q4,R 1,q2,$,q5,R 0,q3,$,q6,R 1,q3,$,q4,R 0,q4,0,q4,R 1,q4,1,q4,R %,q4,%,q7,R 0,q5,0,q5,R 1,q5,1,q5,R %,q5,%,q8,R 0,q6,0,q6,R 1,q6,1,q6,R %,q6,%,q9,R 0,q7,%,q10,R 1,q7,%,q12,R %,q7,%,q7,R 0,q8,%,q11,R 1,q8,%,q10,R %,q8,%,q8,R 0,q9,%,q12,R 1,q9,%,q13,R %,q9,%,q9,R 0,q10,0,q10,R 1,q10,1,q10,R ^,q10,^,q14,R 0,q11,0,q11,R 1,q11,1,q11,R ^,q11,^,q15,R 0,q12,0,q12,R 1,q12,1,q12,R ^,q12,^,q16,R 0,q13,0,q13,R 1,q13,1,q13,R ^,q13,^,q17,R 0,q14,0,q14,R 1,q14,1,q14,R .,q14,0,q0,L 0,q15,0,q15,R 1,q15,1,q15,R .,q15,1,q0,L 0,q16,0,q16,R 1,q16,1,q16,R .,q16,1,q1,L 0,q17,0,q17,R 1,q17,1,q17,R .,q17,0,q1,L