Question

Write the base four representation for 18 to 23 inclusive

Answer 1

`\frac{18}4=4+\frac24`

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


`(18)/(4^2)=(18)/(16)=1+\frac24`

Now divide the remainder by 4 gives


`\frac24=0+\frac24`

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`