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Design a TM to compute addition of two unary numbers
The unary input number n is represented with a symbol 0 n – times.
Example
4 → 0000
1 → 0
5 → 00000
The separation symbol, „#‟ (any other special character) shall be used to distinguish between two or more inputs.
For Example: 5, 2 are the inputs represented by 00000 # 00.
Algorithm
Step 1 - Read the symbols of the first input with no replacements and move right.
Step 2 - When the symbol = ‘#’, replace it by ‘0’ and move right.
Step 3 - Traverse right side until the rightmost ‘0’ (left to B – last symbol)
Step 4 - Replace the rightmost ‘0’ by B
Step 5 - Stop the machine.
Turing Machine
The Turing Machine (TM) is as follows −
The Turing machine, M is given by M = (Q, ∑, Γ, δ, q0, B, F)
Where,
Q = {q0, q1, q2, q3}
Σ = {0, #}
Γ = {0, #, B}
δ ⇒ Given by the above transition diagram q
0 = {q0}
B = {B}
F = {q3}
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