Convert 111 base 2 to 5

Answer 1

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

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

   \[ 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 1 \times 4 + 1 \times 2 + 1 \times 1 = 4 + 2 + 1 = 7_{10} \]

2. Convert from decimal (base 10) to base 5: Now, we need to convert \(7_{10}\) to base 5. To do this, we divide the number by 5 and keep track of the remainders:

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

   Now, we collect the remainders in reverse order of the division:

   The remainders are \(1\) (from the last division) and \(2\) (from the first division), which gives us \(12_5\).

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