Question

1101101 base 2 ÷ 11 base 2

Answer 1

To divide the binary number \( 1101101_2 \) by \( 11_2 \), we will perform binary long division.

1. **Set Up the Division:**
\[
\begin{array}{r|l}
& 1101101 \\
11 & \\
\end{array}
\]

2. **Perform the Division:**
- Divide the first two digits \( 11 \) by \( 11 \):
- \( 11 \) goes into \( 11 \) exactly \( 1 \) time.
- Write down \( 1 \) above the division line.
- Subtract \( 11 \) from \( 11 \):
\[
11 - 11 = 00 \quad \text{(bring down the next digit, which is 0, to make it 000)}
\]

- Now we take the next group, which is \( 000 \).
- \( 11 \) does not go into \( 00 \) (0 times).
- Write down \( 0 \) above the division line.
- Bring down the next \( 1 \) (making it \( 001 \)).
- Again, \( 11 \) does not go into \( 01 \). So we write down another \( 0 \).
- Bring down the next \( 0 \) (which makes it \( 0010 \)).
- Still, \( 11 \) does not go into that, so we write another \( 0 \) again.

- Now we bring down the final \( 1 \) (making it \( 101 \)).
- \( 11 \) goes into \( 10 \) (the first two digits of \( 101 \)) \( 0 \) times.
- Then we take the last \( 1 \) (making it \( 101 \) now).
- \( 11 \) goes into \( 101 \) \( 1 \) time.
- Write down \( 1 \) above the line.
- Then subtract \( 11 \) from \( 101 \):
\[
101 - 11 = 10
\]

- At this point, we have no more digits to bring down. So the remainder is \( 10 \).

3. **Final Result:**
- The quotient is \( 10001_2 \) and the remainder is \( 10_2 \).

Putting it all together, we find:
\[
1101101_2 \div 11_2 = 10001_2 \text{ with a remainder of } 10_2
\]