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Convert the base-64 number \(100_{64}\)  to base 62.

tertre  Mar 20, 2017
 #1
avatar+12565 
0

144 in base 62

ElectricPavlov  Mar 20, 2017
 #2
avatar+19655 
+1

Convert the base-64 number

\(100_{64}\) 

to base 62.

 

\(\begin{array}{lcll} 100_{64} \text{ to base }10\\ \hline (1\cdot 64+0)\cdot 64 + 0 &=& 64^2 \\ &=& 4096_{10} \\ \hline \end{array}\)

 

\(100_{64} = 4096_{10}\)

 

\(\begin{array}{lcll} 4096_{10}\text{ to base } 62 \\ \hline 4096 &:& 62 &=& 66\cdot 62 &+& 4 \\ 66 &:& 62 &=& 1\cdot 62 &+& 4 \\ 1 &:& 62 &=& 0\cdot 62 &+& 1 \\ \hline \end{array} \)

 

\(100_{64} = 4096_{10} = 144_{62}\)

 

laugh

heureka  Mar 20, 2017

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