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.

11001 base 2 to 5

1 answer

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

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