Simplify 110110 base 2 -101101 base 2
To subtract binary numbers, we follow the same rules as subtraction in base 10.
Starting from the rightmost column, we subtract the corresponding digits. If the digit in the second number is larger than the digit in the first number, we "borrow" from the next column by subtracting 1.
In this case, we have:
110110 base 2
- 101101 base 2
______________
011001 base 2
Therefore, 110110 base 2 - 101101 base 2 = 011001 base 2.
To subtract binary numbers, we can use the borrowing method similar to subtracting decimal numbers. Here are the steps to simplify the given expression:
1. Write the two binary numbers in a column format, aligning the corresponding positions:
```
110110
- 101101
```
2. Start subtracting from right to left. Since 0 - 1 is not possible in binary, we need to borrow 1 from the next higher bit, just like in decimal subtraction.
3. Borrowing a 1 from the next higher bit, the first subtraction becomes:
```
110110
- 101101
-------
1001
```
4. Continue subtracting:
```
110110
- 101101
-------
1001
```
5. Finally, the simplified result is 1001 base 2, which is equivalent to 9 in decimal notation.
Therefore, 110110 base 2 - 101101 base 2 simplifies to 1001 base 2.