Question

The sum of the numbers (1110 1111)₂ and (1100 0000)₂ is:

A) (10111 1111)₂
B) (10100 1111)₂
C) (11011 1111)₂
D) (11000 1111)₂

Answer 1

By adding the binary numbers (1110 1111)2 and (1100 0000)2 bit by bit, we find that the correct sum is (11011 1111)2, which corresponds to answer option C.

Step-by-step explanation:

The sum of the binary numbers (1110 1111)2 and (1100 0000)2 can be calculated by adding the two numbers bit by bit from right to left, just as you would with decimal numbers.

1. Add the rightmost digits: 1 + 0 = 1.
2. Move one place to the left: 1 + 0 = 1.
3. Repeat the process for each subsequent pair of digits.
4. When adding the two leftmost digits (1 + 1), you get 102, which means you need to carry the 1.
5. Place the 0 from the result 102 in the current column and carry the 1 to the next left column.
6. After carrying over, you will have an additional digit on the left, leading to the correct sum of (1 1100 1111)2, which in binary notation can also be represented as (1100 1111)2 with the extra bit accounted for.

Therefore, the answer is Option C: (11011 1111)2.