Problem

Convert from binary form to the indicated base.
$1011_{\text {two }}$ to base ten
11
6
22
2022

Answer

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Answer

So, the decimal equivalent of the binary number \(1011_{\text {two }}\) is \(\boxed{11}\)

Steps

Step 1 :Given the binary number \(1011_{\text {two }}\)

Step 2 :We need to convert this binary number to base ten

Step 3 :Starting from the rightmost digit, each digit is multiplied by \(2^n\) where \(n\) is the position of the digit, starting from 0

Step 4 :The first digit from the right is 1, so it is multiplied by \(2^0\) to get 1

Step 5 :The second digit from the right is 1, so it is multiplied by \(2^1\) to get 2

Step 6 :The third digit from the right is 0, so it is multiplied by \(2^2\) to get 0

Step 7 :The fourth digit from the right is 1, so it is multiplied by \(2^3\) to get 8

Step 8 :Adding these values together, we get \(1 + 2 + 0 + 8 = 11\)

Step 9 :So, the decimal equivalent of the binary number \(1011_{\text {two }}\) is \(\boxed{11}\)

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