Converting between Bases

Another example, with a concise solution:

$1758_{10} = 1024 + 512 + 128 + 64 + 16 + 8 + 4 + 2 = 2^{10} + 2^9 + 2^7 + 2^6 + 2^4 + 2^3 + 2^2 + 2^1$

The powers we've used are $10, 9, 7, 6, 4, 3, 2,$ and $1$, so the result is:

$11011011110_2$

Conclusion: $1758_{10}$ is $11011011110_2$ in base 2.

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To convert from base $2$ to base $10$, you do the opposite actions, from right to left:

$110111010_2 = 0\cdot2^0 + 1\cdot2^1 + 0\cdot2^2 + 1\cdot2^3 + 1\cdot2^4 + 1\cdot2^5 + 0\cdot2^6 + 1\cdot2^7 + 1\cdot2^8$

$= 2 + 8 + 16 + 32 + 128 + 256 = 442_{10}$