+1768 Here's how to convert 2231_4 to base 2 without first converting to decimal:
Start with the largest power of 4 that fits into 2231:
4^3 = 64 is the largest power of 4 less than 2231.
Divide 2231 by 64 and get the quotient 34 and the remainder 3.
Write down the quotient 34 as the first digit in the base-2 representation.
Repeat for the remaining digits:
Repeat the process with the remainder 3.
The largest power of 4 that fits into 3 is 4^1 = 4.
Divide 3 by 4 and get the quotient 0 and the remainder 3.
Write down the quotient 0 as the second digit.
Repeat with the remaining 3.
The largest power of 4 that fits into 3 is 4^0 = 1.
Divide 3 by 1 and get the quotient 3 and the remainder 0.
Write down the quotient 3 as the third digit.
Combine the digits:
The digits obtained in the previous steps, in reverse order, give the base-2 representation.
Therefore, 2231_4 in base 2 is 100111_2.
This method directly uses the powers of 4 in the base-4 representation to express the number in the base-2 system, avoiding the need for intermediate decimal conversion.
