Solve the following operation with binary numbers. Check your answer by converting the binary numbers to base 10 numbers, doing the operation on the base 10 numbers, and converting the answer back to base 2.

Question

1112
+ 102

Answer 1

To solve the binary operation of adding 1112 and 102, we start by aligning the numbers vertically:

1112
+ 102
-------

Next, we perform the addition column by column, starting from the rightmost column:

1112
+ 102
-------
110

Since we have a carry-over from the second column, we need to include it in the next column:

1112
+ 102
-------
1010

The final result of 1112 + 102 in binary is 1010.

To check this answer, we can convert the binary numbers to base 10, perform the operation on the base 10 numbers, and convert the result back to base 2:

1112 in base 10 is 7.
102 in base 10 is 2.

Performing the operation 7 + 2 in base 10 gives us 9.

Converting 9 back to binary, we get 1001.

Therefore, our answer of 1010 in the binary operation matches with the result of converting the base 10 numbers.