GATE Overflow Test Series | Mock GATE | Test 5 | Question: 51

Question

Consider the following minimal state finite automata:

Which of the following binary strings is/are accepted by the given automata?

• A. $10010$
• B. $100010001$
• C. $111010101$
• D. $10010000$

Answer 1

The given minimal state finite automata is accepting all binary strings which when interpreted in binary is a multiple of $6.$ Option A is $18$ in decimal and is a multiple of $6.$ Option D is $9 \times 2^4$ and so is a multiple of $6.$ Options B and C are ending in $1$ and so cannot be a multiple of $6.$

So, correct answer: A;D.