Sum of the two binary numbers `(1000010)_(2)` and `(11011)_(2)` is

Options

A. `(111101)_(2)`
B. `(111111)_(2)`
C. `(101111)_(2)`
D. `(111001)_(2)`

Answer

To find the sum of the two binary numbers \( (1000010)_2 \) and \( (11011)_2 \), we can follow these steps:

### Step 1: Align the binary numbers
Align the two binary numbers for addition:
```
1000010
+ 11011
```

### Step 2: Add from right to left
Start adding from the rightmost bit. Remember the rules of binary addition:
- \( 0 + 0 = 0 \)
- \( 0 + 1 = 1 \)
- \( 1 + 0 = 1 \)
- \( 1 + 1 = 10 \) (which means write down 0 and carry over 1)
- \( 1 + 1 + 1 = 11 \) (which means write down 1 and carry over 1)

Let's add the numbers step by step:

1. Rightmost column: \( 0 + 1 = 1 \) (write down 1)
2. Next column: \( 1 + 1 = 10 \) (write down 0, carry over 1)
3. Next column: \( 0 + 0 + 1 = 1 \) (write down 1)
4. Next column: \( 0 + 1 = 1 \) (write down 1)
5. Next column: \( 0 + 1 = 1 \) (write down 1)
6. Next column: \( 1 + 0 = 1 \) (write down 1)
7. Leftmost column: \( 1 + 0 = 1 \) (write down 1)

### Step 3: Write down the result
Putting it all together, we get:
```
1000010
+ 11011
---------
111101
```

Thus, the sum of the two binary numbers \( (1000010)_2 \) and \( (11011)_2 \) is \( (111101)_2 \).

### Final Answer:
The sum is \( (111101)_2 \).

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