Math CentralQuandaries & Queries


Question from anjg, a parent:

How to convert base 4 number 2^11 to base 10 number?

Hi Anjg,

First let's look at $(2_4)^2$ written in base four. Two times two is four and four, written in base four, is $10_4.$ Now try $(2_4)^4$ written in base four. We already know that $(2_4)^2 = 10_4$ so

\[(2_4)^4 = (2_4)^2 \times (2_4)^2 = 10_4 \times 10_4 = 100_4.\]

Continue to write $(2_4)^{11}$ as a base four number without exponents. Finally convert this number to its base 10 form.


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