To convert the decimal number 610 to a binary number, follow these steps:

1. Divide the number by 2 and write down the quotient and remainder.
2. Continue dividing the quotient by 2 until the quotient becomes 0, noting each remainder.
3. The binary representation is obtained by reading the remainders in reverse order (from bottom to top).

Let's go through the steps:

$610 \div 2 = 305 \text{ remainder } 0$ $305 \div 2 = 152 \text{ remainder } 1$ $152 \div 2 = 76 \text{ remainder } 0$ $76 \div 2 = 38 \text{ remainder } 0$ $38 \div 2 = 19 \text{ remainder } 0$ $19 \div 2 = 9 \text{ remainder } 1$ $9 \div 2 = 4 \text{ remainder } 1$ $4 \div 2 = 2 \text{ remainder } 0$ $2 \div 2 = 1 \text{ remainder } 0$ $1 \div 2 = 0 \text{ remainder } 1$

Reading the remainders from bottom to top, we get:

$610_{10} = 1001100010_2$

Thus, the binary representation of 610 is 1001100010.

Would you like further details or have any questions?

Here are 5 related questions for practice:

1. Convert 256 to binary.
2. What is the binary representation of 1023?
3. How do you convert a binary number back to decimal?
4. What is the binary representation of 45?
5. How do you perform binary addition?

Tip: Binary numbers are the foundation of computer processing, representing data using just 0s and 1s!