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To solve the binary addition of \( 111_2 + 11_2 \), we'll follow the rules of binary addition, which are:

1. \( 0 + 0 = 0 \)
2. \( 1 + 0 = 1 \)
3. \( 1 + 1 = 10 \) (which is 0 with a carry of 1)
4. \( 1 + 1 + 1 = 11 \) (which is 1 with a carry of 1)

Let's add these binary numbers step-by-step:

\[
\begin{array}{c@{}c@{}c@{}c@{}c}
  & 1 & 1 & 1 \\
+ & 0 & 1 & 1 \\
\hline
  & 1 & 0 & 1 & 0 \\
\end{array}
\]

**Step-by-Step Addition:**

1. **Rightmost Column:** \(1 + 1 = 10\) (write down 0, carry 1)
2. **Middle Column:** \(1 + 1 + 0 = 10\) (write down 0, carry 1)
3. **Leftmost Column:** \(1 + 1 = 10\) (write down 1)

So, the final result of \(111_2 + 11_2\) in base two is:

\[
1010_2
\]

### Do you want more details or have any questions?

Here are some related questions you might consider:

1. How would you perform subtraction in binary?
2. What is the decimal equivalent of the binary number \(1010_2\)?
3. How can you add three or more binary numbers together?
4. What are some real-world applications of binary arithmetic?
5. What are the rules for multiplying two binary numbers?

**Tip:** When adding binary numbers, always remember to carry over to the next higher bit when the sum of a column exceeds 1.

Learn how to perform binary addition with the example 111_2 + 11_2. This step-by-step guide explains binary carryover and shows the full solution for students learning about base-two systems. Suitable for Grades 6-8.

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