Convert a number 476 with base 10 to a binary by using method one

To convert a decimal number to binary using method one, we need to repeatedly divide the decimal number by 2 until the quotient becomes zero, and then collect the remainders in reverse order.

Step 1: Divide 476 by 2.
$$476 \div 2 = 238$$

Step 2: Divide 238 by 2.
$$238 \div 2 = 119$$

Step 3: Divide 119 by 2.
$$119 \div 2 = 59$$

Step 4: Divide 59 by 2.
$$59 \div 2 = 29$$

Step 5: Divide 29 by 2.
$$29 \div 2 = 14$$

Step 6: Divide 14 by 2.
$$14 \div 2 = 7$$

Step 7: Divide 7 by 2.
$$7 \div 2 = 3$$

Step 8: Divide 3 by 2.
$$3 \div 2 = 1$$

Step 9: Divide 1 by 2.
$$1 \div 2 = 0$$

Now, we collect the remainders in reverse order: 0, 1, 1, 1, 0, 1, 0, 0.

Answer: The binary representation of the decimal number 476 is $$111011100_2$$.