The result of the following addition is ____.(1101.101)2 + (1011.11)2 (11001.111)2 (11001.011)2 (11000.011)2 (1001.011)2

1. Break Down the Problem

We need to perform the binary addition of two numbers:

• $(1101.101)_2$
• $(1011.11)_2$

Following that, we’ll compare the result with the provided options:

• $(11001.111)_2$
• $(11001.011)_2$
• $(11000.011)_2$
• $(1001.011)_2$

2. Relevant Concepts

When adding binary numbers, we align them as we do in decimal addition, starting from the rightmost bit and moving to the left. We have to consider carrying over bits when the sum exceeds $1$ in binary (i.e., $10_2$).

3. Analysis and Detail

Let's perform the binary addition step by step.

1. Align the binary numbers:

         1101.101
       + 1011.110
       ___________
   

2. Start from the rightmost bit:

   • $1 + 0 = 1$ (write down $1$)
   • $0 + 1 = 1$ (write down $1$)
   • $1 + 1 = 10_2$ (write down $0$, carry $1$)
   • $1 + 1 + 1$ (carried over) $= 11_2$ (write down $1$, carry $1$)
   • $1 + 0 + 1$ (carried over) $= 10_2$ (write down $0$, carry $1$)
   • $1 + 1 + 1$ (carried over) $= 11_2$ (write down $1$, carry $1$)
   • Since there’s no more bits in the second number, and we have a carry, we add $1$ at the leftmost position.

Putting it all together, we have:

         1101.101
       + 1011.110
       ___________
      11001.011

4. Verify and Summarize

The binary addition of $(1101.101)_2 + (1011.11)_2$ results in $(11001.011)_2$.

Final Answer

The result of the addition is $(11001.011)_2$.