Question

1001 base 2 to 5

Answer 1

To convert the number \(1001_2\) (in base 2) to base 5, we can follow these steps:

1. **Convert from base 2 to base 10**.
2. **Convert from base 10 to base 5**.

### Step 1: Convert from base 2 to base 10

The binary number \(1001_2\) can be converted to decimal (base 10) using the formula:

\[
\text{{Value}} = d_n \cdot 2^n + d_{n-1} \cdot 2^{n-1} + \ldots + d_0 \cdot 2^0
\]

where \(d\) is the digit in the binary number, and \(n\) is the position of the digit (starting from 0 from the right).

So for \(1001_2\):

\[
1 \cdot 2^{3} + 0 \cdot 2^{2} + 0 \cdot 2^{1} + 1 \cdot 2^{0} = 1 \cdot 8 + 0 \cdot 4 + 0 \cdot 2 + 1 \cdot 1 = 8 + 0 + 0 + 1 = 9
\]

Thus, \(1001_2 = 9_{10}\).

### Step 2: Convert from base 10 to base 5

Now we will convert \(9_{10}\) to base 5 by repeatedly dividing by 5 and recording the remainders.

1. \(9 \div 5 = 1\) with a remainder of \(4\).
2. \(1 \div 5 = 0\) with a remainder of \(1\).

Now we read the remainders from bottom to top. The remainders we have are \(1\) and \(4\) which gives us:

\[
9_{10} = 14_5
\]

### Conclusion

Therefore, \(1001_2\) in base 5 is \(14_5\).