The places in base 4 are ones, fours and sixteens. 2 + 2 = 4
You can't have a four in the ones column, so that becomes one four and zero ones.
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Your question, "Is there any way 2 plus 2 can equal anything but 4?" My answeris YES. If you were to use base 3 math, 2 plus 2 would then equal "11" (base 3) 2 plus 2 = 11 (base 3)
16 plus 10 plus 8 plus 6 plus 2 is equal to 42.
In a binary system, where only the digits 0 and 1 are used, the addition of 2 (represented as 10 in binary) and 2 (also represented as 10 in binary) equals 100 in binary, which is 4 in the decimal system. Therefore, in this specific context, 2 plus 2 equals 11.