To add the numbers \( 100_2 \) and \( 111_2 \) in binary (base 2), follow these steps:

1. **Align the numbers** for addition:
   ```
      0100
   +  0111
   ```

2. **Add column by column** from right to left:
   - **First column** (rightmost): \( 0_2 + 1_2 = 1_2 \).
   - **Second column**: \( 0_2 + 1_2 = 1_2 \).
   - **Third column**: \( 1_2 + 1_2 = 10_2 \). Write down 0 and carry over 1.
   - **Fourth column** (leftmost): \( 0_2 + 0_2 + 1_2 \text{ (carried over)} = 1_2 \).

3. **Write the result** down as follows:
   ```
     1011_2
   ```

Thus, the sum of \( 100_2 \) and \( 111_2 \) in binary is \( 1011_2 \).

---

Would you like more details or have any questions?

Here are some related questions:

1. How do you convert binary numbers to decimal?
2. What is the decimal equivalent of \( 1011_2 \)?
3. How do you subtract binary numbers?
4. What is the process for multiplying two binary numbers?
5. Can you explain how binary addition is used in computer systems?
6. How do you represent the decimal number 5 in binary?
7. What happens when you add \( 1011_2 \) to \( 1001_2 \)?
8. How can binary numbers be used in logical operations?

**Tip:** Binary addition is straightforward because there are only two digits (0 and 1). The key rule is that \( 1_2 + 1_2 \) equals \( 10_2 \), which involves carrying over to the next column.

Learn how to add binary numbers 100 base 2 and 111 base 2 step-by-step. Understand binary addition rules and carry-over concepts with detailed examples. Suitable for Grades 9-12.

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