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# Construct a TM performing multiplication of two unary numbers

## Algorithm

**Step 1 -** Read the leftmost ‘0’ replace it by ‘x’ and move right to process the immediate symbol after ‘#’.

**Step 2 -** Replace the symbol ‘0’ by x and move right reach the first ‘B’ after ‘#’

**Step 3 -** Replace B by ‘0’ and move left until the nearest ‘x’ is reached

**Step 4 -** Replace the ‘x’ by 0 and move right to process the next symbol of the multiplicand.

**Step 5 -** Perform steps 2, 3 and 4 until all the symbols of the multiplicand are processed.

**Step 6 -** Move left to replace the symbol of the multiplier, ‘x’ by ’0’.

**Step 7 -** Perform steps 1 to 6 until all the symbols of the multiplier are processed.

## Turing Machine

The Turing Machine (TM) is as follows

The Turing machine, M is given by

M = (Q, Σ, Γ, δ, q0, B, F)

Where,

Q = {q0, q1, q2, q3, q4, q5, q6}

Σ = {0, #}

Γ = {0, #, x, B}

q0 = {q0}

B = {B}

F = {q6}

δ ⇒ given by the above transition diagram.

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