Question

110 base 2 to 5

Answer 1

To convert the binary number \( 110_2 \) to base 5, you can follow these steps:

1. **Convert from binary (base 2) to decimal (base 10)**:
- Each digit in the binary number represents a power of 2, starting from the right (which represents \( 2^0 \)).
- Thus, \( 110_2 \) can be calculated as:
\[
1 \cdot 2^2 + 1 \cdot 2^1 + 0 \cdot 2^0 = 4 + 2 + 0 = 6_{10}
\]

2. **Convert from decimal (base 10) to base 5**:
- Divide the decimal number by 5 and keep track of the remainders.
- \( 6 \div 5 \) gives a quotient of 1 and a remainder of 1.
- \( 1 \div 5 \) gives a quotient of 0 and a remainder of 1.
- Collect the remainders in reverse order: \( 1, 1 \).

Thus, \( 6_{10} \) is represented as \( 11_5 \).

Therefore, \( 110_2 \) in base 5 is \( 11_5 \).