Convert 111 base 2 to 5

Answer 1

To convert the binary number \( 111_2 \) to base 5, we can follow these steps:

1. Convert from base 2 to base 10: The binary number \( 111_2 \) can be converted to decimal by calculating:

   \[ 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 1 \times 4 + 1 \times 2 + 1 \times 1 = 4 + 2 + 1 = 7 \]

   So, \( 111_2 \) is \( 7_{10} \).

2. Convert from base 10 to base 5: Now we will convert \( 7_{10} \) to base 5. We do this by dividing the number by 5 and keeping track of the remainders:

   • \( 7 \div 5 = 1 \) with a remainder of \( 2 \)
   • \( 1 \div 5 = 0 \) with a remainder of \( 1 \)

   Now, we read the remainders from bottom to top. Therefore, combining these gives us:

   \[ 7_{10} = 12_5 \]

So, the binary number \( 111_2 \) is equal to \( 12_5 \) in base 5.