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 \( 11_5 \).

110 base 2 to 5

1 answer

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

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: \[ 1 \cdot 2^2 + 1 \cdot 2^1 + 0 \cdot 2^0 = 4 + 2 + 0 = 6_{10} \]
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 \( 11_5 \).