Question 9
7.7
Convert from binary form to the indicated base.
$10100000111_{\text {two }}$ to base ten
1287
$20,200,000,222$
2574
10
Answer
The base ten equivalent of the binary number \(10100000111_{\text {two }}\) is \(\boxed{1287}\).
Step 1 ：The question is asking to convert a binary number to base ten. The binary number system is base 2, and each digit represents a power of 2, starting from 0 at the rightmost digit (least significant bit).
Step 2 ：To convert a binary number to decimal, we can multiply each digit of the binary number by 2 raised to the power of its position, and sum up all these values.
Step 3 ：The binary number given in the question is \(10100000111_{\text {two }}\). Let's convert this to base ten.
Step 4 ：The base ten equivalent of the binary number \(10100000111_{\text {two }}\) is \(\boxed{1287}\).
