Questions: Convert the following base 10 numeral to a base 2 numeral and enter your answer in the box. 40 Base 2 numeral:

Solution Steps

To convert a base 10 numeral to a base 2 numeral, we can repeatedly divide the number by 2 and keep track of the remainders. The binary representation is obtained by reading the remainders in reverse order.

To convert the decimal number \( 40 \) to binary, we repeatedly divide by \( 2 \) and record the remainders. The process is as follows:

1. \( 40 \div 2 = 20 \) with a remainder of \( 0 \)
2. \( 20 \div 2 = 10 \) with a remainder of \( 0 \)
3. \( 10 \div 2 = 5 \) with a remainder of \( 0 \)
4. \( 5 \div 2 = 2 \) with a remainder of \( 1 \)
5. \( 2 \div 2 = 1 \) with a remainder of \( 0 \)
6. \( 1 \div 2 = 0 \) with a remainder of \( 1 \)

Reading the remainders from bottom to top gives us the binary representation.

The binary representation of \( 40 \) is obtained by reading the remainders in reverse order: \( 101000 \).

Final Answer