Final answer:
Binary addition involves rules where a '1' carry-over from the last digit adds an extra digit to the left. The adding process follows a simple set of rules, and any carry at the end results in an increased length of the final binary number.
Step-by-step explanation:
The student's question appears to be about binary addition and specifically what happens if there is a '1' that carries over at the end of the addition process. In binary addition, just as with decimal addition, if a '1' needs to be carried over after the last digit, you simply add an extra digit to the left. For example, when adding 1 + 1 in binary, the result is 10, where '1' is the carry-over, becoming the next leftmost digit.
In binary addition, the rules are as follows:
- 0 + 0 = 0
- 0 + 1 = 1
- 1 + 0 = 1
- 1 + 1 = 10 (0 with a carry of 1)
When you are adding two binary numbers and the final calculation involves a carry, such as adding 1111 + 0001:
- 1 + 1 = 10, so you write down 0 and carry the 1.
- 1 + 1 (carried) + 1 = 11, so you write down 1 and carry the 1.
- 1 (carried) + 1 = 10, so you write down 0 and carry the 1.
- Finally, 1 (carried) + 1 = 10, and since there are no more digits to add to, you write both digits down, making the final result 10000.
This example shows that the additional carry increases the length of the resultant binary number by one digit, similar to how a carry in decimal addition can increase the number of digits by one.