To convert the decimal number $1386$ to a binary number, we follow the division by 2 method:

1. Divide 1386 by 2:
   $1386 \div 2 = 693$ remainder $0$
2. Divide 693 by 2:
   $693 \div 2 = 346$ remainder $1$
3. Divide 346 by 2:
   $346 \div 2 = 173$ remainder $0$
4. Divide 173 by 2:
   $173 \div 2 = 86$ remainder $1$
5. Divide 86 by 2:
   $86 \div 2 = 43$ remainder $0$
6. Divide 43 by 2:
   $43 \div 2 = 21$ remainder $1$
7. Divide 21 by 2:
   $21 \div 2 = 10$ remainder $1$
8. Divide 10 by 2:
   $10 \div 2 = 5$ remainder $0$
9. Divide 5 by 2:
   $5 \div 2 = 2$ remainder $1$
10. Divide 2 by 2:
    $2 \div 2 = 1$ remainder $0$
11. Divide 1 by 2:
    $1 \div 2 = 0$ remainder $1$

Now, take the remainders from the last to the first:

So, $1386_{10} = 10101101010_2$.

Would you like more details on binary conversions or have any questions?

Here are 5 related questions to expand on this concept:

1. How do you convert binary numbers back to decimal?
2. What is the binary equivalent of $543$?
3. How does binary addition work between two numbers?
4. What is the largest number you can represent with 8 bits in binary?
5. Can you explain how negative numbers are represented in binary using two's complement?

Tip: To quickly verify a binary conversion, convert it back to decimal by multiplying each bit by $2^n$, where $n$ is the bit's position from right to left, starting from 0.