Question

11001 base 2 to 5

Answer 1

To convert the binary number \( 11001_2 \) to base 5, we can follow these steps:

1. **Convert from Binary (Base 2) to Decimal (Base 10)**:
The binary number \( 11001_2 \) can be converted to decimal using the place values of binary (which are powers of 2):

\[
1 \times 2^4 + 1 \times 2^3 + 0 \times 2^2 + 0 \times 2^1 + 1 \times 2^0
\]
\[
= 1 \times 16 + 1 \times 8 + 0 \times 4 + 0 \times 2 + 1 \times 1
\]
\[
= 16 + 8 + 0 + 0 + 1 = 25
\]

So, \( 11001_2 = 25_{10} \).

2. **Convert from Decimal (Base 10) to Base 5**:
Now we convert \( 25_{10} \) to base 5 by repeatedly dividing by 5 and noting the remainders.

\[
25 \div 5 = 5 \quad \text{(remainder 0)}
\]
\[
5 \div 5 = 1 \quad \text{(remainder 0)}
\]
\[
1 \div 5 = 0 \quad \text{(remainder 1)}
\]

Collecting the remainders from bottom to top gives us \( 100_5 \).

Therefore, \( 11001_2 \) is equivalent to \( 100_5 \) in base 5.