Question

Выполните сложение 1011 (2 снизу) + 101 (2 снизу)=?проверьте правильность выполнения операции, сложения переводом слагаемых и результата - десятичную систему счисления.с решением пожалуйста\

Answer 1

Addition in Binary System

To perform the addition of the numbers 1011 (in base 2) and 101 (in base 2), we need to add the corresponding digits from right to left, just like in decimal addition. Here's the step-by-step process:

1. Start by adding the rightmost digits: 1 + 1 = 10. Write down the 0 and carry over the 1 to the next column. 2. Move to the next column and add the digits: 1 + 0 + 1 = 10. Write down the 0 and carry over the 1. 3. Proceed to the next column: 1 + 1 + 0 = 10. Write down the 0 and carry over the 1. 4. Finally, add the leftmost digits: 1 + 0 + 0 = 1. Write down the 1.

The result of the addition is 11000 (in base 2).

To verify the correctness of the addition, let's convert the binary numbers to decimal and perform the addition in the decimal system:

- 1011 (in base 2) is equal to 11 (in base 10). - 101 (in base 2) is equal to 5 (in base 10).

Adding 11 and 5 in the decimal system gives us 16.

Therefore, the result of the addition 1011 (in base 2) + 101 (in base 2) is indeed 11000 (in base 2), which is equal to 16 in the decimal system.

Note: The source provides a snippet from the "Kvant Journal," but it doesn't seem to be directly related to the question at hand.