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Question Number 35072 by Rasheed.Sindhi last updated on 15/May/18

$$\mathrm{An}\mathrm{n}-\mathrm{digit}\mathrm{decimal}\mathrm{number}\mathrm{has}\mathrm{been}$$$$\mathrm{conveerted}\mathrm{into}\mathrm{octal}\mathrm{number}.\mathrm{Say}\mathrm{it}$$$$\mathrm{has}\mathrm{m}\mathrm{digits}.\mathrm{What}\mathrm{are}\mathrm{possible}\mathrm{minimum}$$$$\mathrm{and}\mathrm{maximum}\mathrm{values}\mathrm{of}\mathrm{m}\mathrm{in}\mathrm{terms}\mathrm{of}$$$$\mathrm{n}?$$

Commented by candre last updated on 15/May/18

$$min\Rightarrow num={10}^{n-1}$$$$min=\lfloor {\log }_8\left({10}^{n-1}\right)\rfloor +1=\lfloor (n-1){\log }_{8}10\rfloor +1$$$$max\Rightarrow num={10}^n-1$$$$max=\lfloor {\log }_8({10}^n-1)\rfloor +1$$

Commented by Rasheed.Sindhi last updated on 15/May/18

$$\mathcal{T}h\alpha nk\mathcal{S}alotSir!$$

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