Perform the following binary operations and show all your work. 
a. 11110100 + 11001010

Let's perform the binary addition of \( 11110100 \) and \( 11001010 \). I will walk through each step, showing how to add binary numbers. 

### Step 1: Align the binary numbers
```
   11110100
+  11001010
```

### Step 2: Add each bit from right to left, carrying over when the sum is 2 (just like in decimal addition).

**Bit-by-bit addition:**
1. \( 0 + 0 = 0 \) (No carry)
2. \( 0 + 1 = 1 \) (No carry)
3. \( 1 + 0 = 1 \) (No carry)
4. \( 0 + 1 = 1 \) (No carry)
5. \( 1 + 0 = 1 \) (No carry)
6. \( 1 + 1 = 10 \) → Write down 0 and carry over 1.
7. \( 1 + 1 = 10 \) plus carry 1 → \( 10 + 1 = 11 \) → Write down 1 and carry over 1.
8. \( 1 + 1 = 10 \) plus carry 1 → \( 10 + 1 = 11 \) → Write down 1 and carry over 1.

### Step 3: If there’s still a carry at the end, write it down as an extra bit.

```
   11110100
+  11001010
------------
  110111110
```

### Final Answer:
The sum of \( 11110100 \) and \( 11001010 \) in binary is \( 110111110 \).

Would you like further details on how binary addition works, or is there anything else you'd like to clarify?

Here are 5 additional questions based on this topic:
1. How do you perform binary subtraction?
2. Can you explain how binary multiplication works?
3. What happens when you add binary numbers larger than 8 bits?
4. How can binary addition be used in computers for arithmetic operations?
5. What is binary overflow and when does it occur?

**Tip:** In binary, whenever you get a sum of 2, you write down 0 and carry over 1, similar to how in decimal, you carry over when the sum is 10.

Perform the following binary operations and show all your work. a. 11110100 + 11001010

Learn how to add two binary numbers, 11110100 and 11001010, with a detailed step-by-step breakdown. This problem explores binary addition concepts and the carrying rule in binary arithmetic, suitable for students in Grades 5-8.

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