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.
1100102
- 10102
To solve the subtraction of binary numbers, we can use the borrowing method just like in decimal subtraction.
First, let's align the numbers:
110010
- 1010
---------
Now, starting from the rightmost digit, subtract each pair of digits. If the digit on the bottom is larger than the digit on top, we need to borrow from the next column.
110010
- 1010
---------
101000
In this case, there are no borrows needed, so we can subtract directly:
First, subtract 0 from 0, which gives us 0:
110010
- 1010
---------
101000
0
Then, subtract 1 from 1, which gives us 0:
110010
- 1010
---------
101000
0
Continue this process for the remaining digits:
110010
- 1010
---------
101000
0
The final result of the subtraction in binary is 101000.
To check our answer, let's convert the binary numbers to base 10, do the subtraction operation with base 10 numbers, and convert the answer back to base 2:
110010 in base 2 is equal to 50 in base 10.
1010 in base 2 is equal to 10 in base 10.
Subtracting 10 from 50, we get:
50 - 10 = 40
Converting 40 back to base 2, we get:
40 in base 10 is equal to 101000 in base 2.
So, our answer is correct. The binary subtraction 110010 - 1010 equals 101000.
To subtract binary numbers, follow these steps:
Step 1: Write down the two binary numbers vertically, lining up the corresponding digits (from right to left).
110010
- 1010
Step 2: Start from the rightmost digit and subtract the two binary digits.
1
- 1
-----
0
Step 3: Move to the next digit and subtract the corresponding digits.
1
- 0
-----
1
Step 4: Continue the process until all digits have been subtracted.
1
- 0
-----
1
1
- 1
-----
0
0
- 0
-----
0
Step 5: Write down the final result.
110010
- 1010
------
101000
To check if the answer is correct, we can convert the binary numbers to base 10, perform the subtraction in base 10, and convert the answer back to base 2.
Converting the binary numbers to base 10:
Binary 1100102 = 50 (base 10)
Binary 10102 = 10 (base 10)
Performing the subtraction in base 10: 50 - 10 = 40
Converting the base 10 answer to binary:
Decimal 40 = 1010002
The calculated binary answer matches the answer obtained by converting the binary numbers to base 10 and performing the subtraction, which confirms the correctness of the initial subtraction.