100101 + 101 + 1101 + 100 is equal to:

Options

A. 1101001
B. 100000
C. 111011
D. None of these

Answer

To solve the binary addition of the numbers 100101, 101, 1101, and 100, we will follow a step-by-step approach.

### Step 1: Align the Numbers
First, we need to write the numbers in a column format, aligning them to the right:

```
100101
101
1101
100
```

### Step 2: Add the Rightmost Column
Starting from the rightmost column, we add the digits:
- 1 (from 100101)
- 1 (from 101)
- 1 (from 1101)
- 0 (from 100)

Adding these gives us:
1 + 1 + 1 + 0 = 3 in decimal, which is 11 in binary. We write down 1 and carry over 1.

### Step 3: Move to the Next Column
Next, we move to the second column from the right:
- 0 (from 100101)
- 0 (from 101)
- 0 (from 1101)
- 1 (from 100)
- Plus the carry of 1 from the previous column.

Adding these gives us:
0 + 0 + 0 + 1 + 1 = 2 in decimal, which is 10 in binary. We write down 0 and carry over 1.

### Step 4: Move to the Next Column
Now, we move to the third column from the right:
- 1 (from 100101)
- 1 (from 101)
- 1 (from 1101)
- 0 (from 100)
- Plus the carry of 1 from the previous column.

Adding these gives us:
1 + 1 + 1 + 0 + 1 = 4 in decimal, which is 100 in binary. We write down 0 and carry over 2.

### Step 5: Move to the Fourth Column
Next, we move to the fourth column from the right:
- 0 (from 100101)
- 0 (from 101)
- 1 (from 1101)
- 0 (from 100)
- Plus the carry of 2 from the previous column.

Adding these gives us:
0 + 0 + 1 + 0 + 2 = 3 in decimal, which is 11 in binary. We write down 1 and carry over 1.

### Step 6: Move to the Fifth Column
Now, we move to the fifth column from the right:
- 1 (from 100101)
- 0 (from 101)
- 0 (from 1101)
- 0 (from 100)
- Plus the carry of 1 from the previous column.

Adding these gives us:
1 + 0 + 0 + 0 + 1 = 2 in decimal, which is 10 in binary. We write down 0 and carry over 1.

### Step 7: Move to the Sixth Column
Finally, we move to the sixth column from the right:
- 1 (from 100101)
- No other digits to add.
- Plus the carry of 1 from the previous column.

Adding these gives us:
1 + 1 = 2 in decimal, which is 10 in binary. We write down 0 and carry over 1.

### Step 8: Write the Final Carry
Since we have a carry of 1 left, we write it down as the leftmost digit.

### Final Result
Putting all the results together, we have:

```
100101
101
1101
100
--------
1100110
```

Thus, the final result of the binary addition is **1100110**.

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