In our decimal system, we distinguish odd and even numbers by looking at their ones (or units) digits. If the ones digit is even (0, 2, 4, 6, 8), the number is even. If the ones digit is odd (1, 3, 5, 7, 9), the number is odd. Determine whether this same criterion works for numbers expressed in base four

Yes. In base 4 numbers if a number ends with 0 or 2 then it is an even number. If it ends with 1 or 3 then it is an odd number.

Step-by-step explanation:

The first 13 numbers in base 4 are written in brackets next to their corrsponding decimal number below

decimal number 0(0) ,1 (1) ,2(2), 3(3), 4(10), 5(11), 6(12), 7(13), 8,(20), 9(21), 10(22), 11(23), 12(30), 13(31) and so on

From above we can deduce that in base-4 any number ending with 0 or 2 is an even nmuber and any number ending with 1 or 3 is an odd number