Question

Convert $(1401{)}_5$ to base $2$

• A. $(11100010{)}_2$
• B. $(226{)}_2$
• C. $(10110110{)}_2$
• D. $(294{)}_2$

Answer 1

The correct option is A $(11100010{)}_2$

Let us first convert $1401$ to base $10$ as follows:

$1\times 5^3=1\times 125=125$

$4\times 5^2=4\times 25=100$

$0\times 5^1=0\times 5=0$

$1\times 5^0=1\times 1=1$

Adding all, we get $125+100+0+1=226$

Therefore, $(1401{)}_5=(226{)}_{10}$

Now, we convert $226$ base $10$ into base $2$ by dividing $226$ by $2$.

The equation calculation formula for $226$ number to $2$ is like shown below.

$2|2262|113|02|56|12|28|02|14|02|7|02|3|12|1|1$

From the above steps of division and remainders we conclude that the required number is $11100010$ base $2$.

Hence, $(1401{)}_5=(11100010{)}_2$