# Converting to base $-2$

How to convert a number given in Decimal to negative base.?

For eg I want to convert $67$ given in decimal base to base $-2$.?

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You might enjoy en.wikipedia.org/wiki/Quater-imaginary_base, which discusses an imaginary base system. –  Snowball Oct 26 '12 at 22:08
I've removed algebra tag, since we don't use algebra tag anymore, see meta for details –  Martin Sleziak Oct 27 '12 at 6:27

$67 = \color{red}1 \cdot (-2)^6 + \color{red}0 \cdot (-2)^5 + \color{red}0 \cdot (-2)^4 + \color{red}0 \cdot (-2)^3 + \color{red}1 \cdot (-2)^2 + \color{red}1 \cdot (-2)^1 + \color{red}1 \cdot (-2)^0$, so $67_{10} = 1000111_{-2}$.
An interesting feature of this base system is that you can represent negative numbers without a minus sign. For example, $-67_{10} = 11001101_{-2}$.