The problem asks to simplify $(11_{two})^2$. The answer should be expressed in base 2.

1. Problem Description

The problem asks to simplify $(11_{two})^2$. The answer should be expressed in base

2.

2. Solution Steps

First, convert $11_{two}$ to base

1

0. $11_{two} = 1 \cdot 2^1 + 1 \cdot 2^0 = 2 + 1 = 3$.

Now, square the result in base 10:

$3^2 = 9$.

Finally, convert 9 to base 2:

$9 = 8 + 1 = 1 \cdot 2^3 + 0 \cdot 2^2 + 0 \cdot 2^1 + 1 \cdot 2^0$.

Therefore, $9_{ten} = 1001_{two}$.

3. Final Answer

A. $1001_{two}$