Question

Write the base four representation for 18 to 23 inclusive

Answer 1

$\dfrac{18}4=4+\dfrac24$

which means 18 can be divided by a higher power of 4 to get a quotient smaller than 4. Indeed,

$\dfrac{18}{4^2}=\dfrac{18}{16}=1+\dfrac24$

Now divide the remainder by 4 gives

$\dfrac24=0+\dfrac24$

and so

$18_{10}=102_4$

Now the next four numbers are easy to find.

$19_{10}=103_4$
$20_{10}=110_4$
$21_{10}=111_4$
$22_{10}=112_4$
$23_{10}=113_4$