Design a TM to compute addition of two unary numbers

Data Structure AlgorithmsComputer ScienceComputers

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}

raja
Updated on 15-Jun-2021 12:08:55

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