Question

what is 23 base 4 plus 21 base 4?

Answer 1

1+3 = 4

but 4 doesn't exist in base 4 (much like the number 10 as a single digit doesn't exist in base 10)

so this means 1+3 = 10 in base 4

Answer 2

2+2 = 10 in base 4 as well

and we also have a carry over, so we really have

1+2+2 = 1+10 = 11 base 4

Answer 3

put this all together to get