## How many states required for DFA which accepts set of all strings are divisible by 5 for binary alphabet 0 1?

So, 5 states for 5 remainder values. After processing a string ω if end-state becomes q0 that means decimal equivalent of input string is divisible by 5.

## Can this DFA accept string 101?

In the given solution, we can see that only input 101 will be accepted. Hence, for input 101, there is no other path shown for other input.

**What are the minimum of a DFA to accept a binary number divisible by 3?**

The DFA for given problem is : As, when a number is divided by 3, there are only 3 possibilities. The remainder can be either 0, 1 or 2. Here, state 0 represents that the remainder when the number is divided by 3 is 0.

**How do you know if a binary number is divisible by 3 DFA?**

Basically count the number of non-zero odd positions bits and non-zero even position bits from the right. If their difference is divisible by 3, then the number is divisible by 3. For example: 15 = 1111 which has 2 odd and 2 even non-zero bits.

### How do you know if a binary string is divisible by 5?

If the number goes to five or above you subtract five. If you end up with 0 the number is divisible by 5.

### How many states a DFA has if it accept all binary strings divisible by 3 and 2?

Explanation: In this DFA there are three states q0, q1, q2, q3 and the input is strings of {0, 1} which is interpreted as binary number. The state q0 is final state and q1, q2, q3 are non-final state.

**Can this DFA accepts string 010?**

Strings over the binary alphabet that do not contain the substring 010. The condition here is that the substring 010 is not permitted, but other combinations such 000,011,001 are permitted.

**Can this DFA accept string 01111?**

Hence, when i>1, make a transition of “0” from state “C” to state “B” and make a transition of “1” from the state “E” to state “D”. Hence, strings like 010111, 011111, 0101111111, etc. are acceptable now.

#### How do you know if a binary number is divisible by 5?

#### What is DFA explain with an example?

DFA refers to deterministic finite automata. Deterministic refers to the uniqueness of the computation. The finite automata are deterministic FA, if the machine reads an input string one symbol at a time. In DFA, there is only one path input from the current state to the next state.

**How do you know a number is divisible by 5?**

Divisibility by 5 is easily determined by checking the last digit in the number (475), and seeing if it is either 0 or 5. If the last number is either 0 or 5, the entire number is divisible by 5. If the last digit in the number is 0, then the result will be the remaining digits multiplied by 2.

**How a binary number is divisible by 4?**

We have to find out which of the given binary numbers are divisible by ‘4’ . For this, we divide each of the given numbers by 4 and the number whose remainder is zero will be the one which is divisible by 4. From the above calculations, it is clear that ‘100101100’ is the only binary number which is divisible by 4.

## How do you know a number is divisible by 4?

To check whether a number is divisible by 4, just divide the last two digits of the number by 4. If the result is a whole number, then the original number is divisible by 4. A number is divisible by 8 if its last three digits are divisible by 8.

## What is the number of states required if string starts with 0101?

(b) The language { w ∈ Σ∗ | w contains the substring 0101, i.e., w = x0101y for some x, y ∈ Σ∗ } with five states.

**Can this DFA accept string?**

This DFA does not accept any string because it has no accepting state. Thus the language it accepts is the empty set .

**How many states require string ends with 10?**

3. Number of states require to accept string ends with 10. d) can’t be represented.

### How do you know if a binary number is divisible by a binary number?

Efficient Approach: In the binary string, check for the last k bits. If all the last k bits are 0, then the binary number is evenly divisible by 2k else it is not evenly divisible.

### How are DFA processes strings?

Then first we shall check the transition δ (q0, S1) = q1 where q1 is the state where DFA reaches from q0 by input of S1 where DFA reaches from q0 by input. Then we apply δ(qi-1, Si) = qi for each i. If qn ∈ F then the input S1, S2, S3, ….. Sn is accepted otherwise the string is rejected.

**Which string is accepted by DFA?**

A string w is accepted by a DFA < Q , , q0 , , A > , if and only if *( q0 , w ) A . That is a string is accepted by a DFA if and only if the DFA starting at the initial state ends in an accepting state after reading the string.

**How do you calculate divisibility?**

First, take any number (for this example it will be 492) and add together each digit in the number (4 + 9 + 2 = 15). Then take that sum (15) and determine if it is divisible by 3. The original number is divisible by 3 (or 9) if and only if the sum of its digits is divisible by 3 (or 9).

#### Is 45 divisible by 3 yes or no?

As we already know that 45 is divisible by 3, we will see that the sum of its digits are a multiple of 3. 9 is divisible by 3 therefore 45 is also divisible by 3.

#### How do you know if a binary number is divisible by 6?

A number is divisible by 6 it’s divisible by 2 and 3. a) A number is divisible by 2 if its last digit is divisible by 2. b) A number is divisible by 3 if sum of digits is divisible by 3.

**Is 96 divisible by 4 yes or no?**

Step 5: Since 96 is divisible by 2 it is also divisible by 4.

**What is the divisibility rule for 6?**

Rule for 6: If a number is divisible by 2 and 3 the number is divisible by 6. This means 6 will divide any even number whose digits sum to a multiple of 3.

## How many states require the string ending with 001?

Hence, 4 states will be required.