Convert 4\(_2\) to a number in base two

To convert a number in base 4 to base 2, we first need to convert it to base 10, and then from base 10 to base 2. To convert 4\(_2\) to base 10, we start from the rightmost digit and multiply each digit by the corresponding power of 4 and then add the results. 4\(_2\) = 4 x 2\(^0\) = 4 Now that we have converted 4\(_2\) to base 10 and found that it equals 4, we can convert it to base 2. To do this, we divide 4 by 2 and keep track of the remainders until we get a quotient of 0. Then we write the remainders in reverse order to get the base 2 equivalent. 4 / 2 = 2 remainder 0 2 / 2 = 1 remainder 0 1 / 2 = 0 remainder 1 The remainders in reverse order are 1 0 0, which gives us the base 2 equivalent of 4\(_2\): 4\(_2\) = 100\(_2\) Therefore, the answer is 100.