11110 base 2 to 5

Answer 1

To convert the binary number \( 11110_2 \) 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 \( 11110_2 \) can be converted to decimal (base 10) by applying the formula:

\[ n = b_k \cdot 2^k + b_{k-1} \cdot 2^{k-1} + ... + b_1 \cdot 2^1 + b_0 \cdot 2^0 \]

where \( b_k \) are the binary digits (from left to right).

So for \( 11110_2 \):

\[ 11110_2 = 1 \cdot 2^4 + 1 \cdot 2^3 + 1 \cdot 2^2 + 1 \cdot 2^1 + 0 \cdot 2^0 \] \[ = 1 \cdot 16 + 1 \cdot 8 + 1 \cdot 4 + 1 \cdot 2 + 0 \cdot 1 \] \[ = 16 + 8 + 4 + 2 + 0 = 30 \]

Step 2: Convert from base 10 to base 5

Now we convert \( 30_{10} \) to base 5 by repeatedly dividing by 5 and recording the remainders.

1. \( 30 \div 5 = 6 \) remainder \( 0 \)
2. \( 6 \div 5 = 1 \) remainder \( 1 \)
3. \( 1 \div 5 = 0 \) remainder \( 1 \)

Now, read the remainders from bottom to top:

So, \( 30_{10} = 110_5 \).

Final Result

Therefore, the binary number \( 11110_2 \) is equal to \( 110_5 \) in base 5.