Performing binary addition:
To perform binary addition, we follow a set of rules similar to decimal addition. The rules are as follows:

- 0 + 0 = 0
- 0 + 1 = 1
- 1 + 0 = 1
- 1 + 1 = 10 (carry 1 and write 0)

Given binary numbers: 101101 and 011011

Let's perform the addition step by step:

Step 1: Start from the rightmost bit and add the corresponding bits.
1
0 1 1 0 1 0 1 (101101)
+ 0 1 1 0 1 1 (011011)
----------------
1 0 0 1 0 0 0 (1001000)

Step 2: Carry over any 1s to the next column (if applicable).
1
0 1 1 0 1 0 1 (101101)
+ 0 1 1 0 1 1 (011011)
----------------
1 0 0 1 0 0 0 (1001000)

Since there are no more columns to add, we have our final result:

101101 + 011011 = 1001000

Therefore, the correct answer is option 'D' (1001000).

In binary addition, each bit represents a power of 2, where the rightmost bit is 2^0, the second rightmost bit is 2^1, the third rightmost bit is 2^2, and so on. By adding the corresponding bits, we calculate the sum of each power of 2. If there is a carry (1), it is added to the next column.

In this case, we have a carry in the fourth column, so we carry over the 1 to the next column. The final result is obtained by combining all the bits together, from left to right.