Convert 110 base 3 to 8

Answer 1

To convert the number \( 110_3 \) (base 3) to base 8, we can follow these steps:

1. Convert from base 3 to base 10: \[ 110_3 = 1 \cdot 3^2 + 1 \cdot 3^1 + 0 \cdot 3^0 \] \[ = 1 \cdot 9 + 1 \cdot 3 + 0 \cdot 1 \] \[ = 9 + 3 + 0 = 12_{10} \]

2. Convert from base 10 to base 8: Now, we convert \( 12_{10} \) to base 8. We divide by 8: \[ 12 \div 8 = 1 \quad \text{remainder} \quad 4 \] So, \( 12_{10} = 14_8 \).

Putting it all together, the final answer is: \[ 110_3 = 14_8 \]