7. $[\mathbf{3}]$ Express -2013 in base -4 .
Answer: $200203-2013 \equiv 3(\bmod 4)$, so the last digit is $3 ;$ now $\frac{-2013-3}{-4}=504 \equiv 0$, so the next digit (to the left) is 0 ; then $\frac{504-0}{-4}=-126 \equiv 2 ; \frac{-126-2}{-4}=32 \equiv 0 ; \frac{32-0}{-4}=-8 \equiv 0 ; \frac{-8-0}{-4}=2$.
Thus $-2013_{10}=200203_{-4}$.