DFA Example : Construct The Minimal Finite Automata That Accepts All Base 8 Numbers Which Are Divisible By ‘6’

Construct The Minimal Finite Automata That Accepts All Base 8 Numbers Which Are Divisible By ‘6’

(Binary Means Base 2, i.e Σ(0,1) Input Symbols Will Be 2 Only 0 & 1)

(Integer Means Base 10,i.e (0,1,2,3,4,5,6,7,8,9) Input Symbols Will Be 10 Only 0&1&2&3&4&5&6&7&8&9)

Here Given Input Symbols Are Base ‘8’, It Means OCTAT.

My Input Symbols Are Σ={0,1,2,3,4,5,6,7}

Example :- (22)₈

= (2×8¹+2×8⁰)₁₀

=(16+2)₁₀

=(18)

After Conversion Into Decimal (22)₈ Is Divisible By ‘6’

Possible Remainders For ‘6’

Question Is Divisible By ‘6’

Means Remainder Should Be ‘0’

For ‘0’ We Gave ‘q₀‘As State ,  ‘q₀‘ Is Final State.

q₁= q₄

q₂=q₅

q₁& q₄ Are Same, I’ll Merge Both.

q₁= q₄

q₂ & q₅ 

Are Same, I’ll Merge Both.

q₂=q₅

No Commons States In This Table.

MAKE DFA USING THIS TABLE.

DFA Is Ready.

Now Take Any Number Which Has Base 8, Which Is Divisible By ‘6’

Example:- (22)₈

If I Give ‘2’ To ‘q₀‘ , I’ll Go To ‘q₂‘

If I Give ‘2’ To ‘q₂‘, I’ll Go To ‘q₀‘(Final State)

Hence Satisfied.

TYPES OF PROBLEMS WE SOLVED TILL NOW.

1. BINARY(INPUT SYMBOL) – (0,1)
2. INTEGER (INPUT SYMBOL) – (0,9)
3. BASE 8, OCTAT (INPUT SYMBOL) – (0-7)