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.
1112
+ 102
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.
To solve the binary operation, we can follow these steps:
Step 1: Add the two binary numbers column by column from right to left.
Step 2: If the sum in each column is greater than 1, we need to carry over to the next column.
Step 3: Write down the final sum of each column.
Let's solve the operation:
1 1 1
+ 1 0 2
___________
1 0 1 4
The final sum is 1 0 1 4 in binary.
To check our answer, let's convert the binary numbers to base 10, perform the operation in base 10, and convert the answer back to binary:
1112 in base 2 is equal to 14 in base 10.
102 in base 2 is equal to 2 in base 10.
Performing the addition in base 10 gives us 14 + 2 = 16.
Now, let's convert 16 in base 10 back to binary:
16 in base 10 is equal to 1 0 0 0 in base 2.
As we can see, our answer from the binary addition (1 0 1 4) matches the answer when converting base 10 numbers to binary and performing the operation (1 0 0 0).