Question

In our number system the base is ten. If the base were changed to four you would count as follows: $1,2,3,10,11,12,13,20,21,22,23,30,....$ The twentieth number would be:

• A. $20$
• B. $38$
• C. $44$
• D. $104$
• E. $110$

Answer 1

The correct option is E $110$

If we change the base from 10 to 4 then the number 20 will be written as

$20$= $1\times 4^2$+$1\times 4^1$+$0\times 4^0$.

so the required number is 110.

we can also find by dividing the number by 4

$\frac{20}{4}$ =$5$. now $\frac{5}{4}$=1 as dividend, now $\frac{1}{4}$=0 as dividend. so the required number is 110.

so option $E$ is correct option.