Sum of Powers of Two

Every positive integer can be expressed in a unique way as the sum of powers of $2$. Express $2008$ as the sum of powers of $2$.
Source: NCTM Mathematics Teacher 2008

SOLUTION
$2^{11}=2048$
$2^{10}=1024$
$2008-2^{10}=984$
$2^9=512$
$2008-2^{10}-2^9=472$
$2^8=256$
$2008-2^{10}-2^9-2^8=216$
$2^7=128$
$2008-2^{10}-2^9-2^8-2^7=88$
$2^6=64$
$2008-2^{10}-2^9-2^8-2^7-2^6=24$
$2^4=16$
$2008-2^{10}-2^9-2^8-2^7-2^6-2^4=8$
$2^3=8$
$2008-2^{10}-2^9-2^8-2^7-2^6-2^4-2^3=0$
$2008=2^{10}+2^9+2^8+2^7+2^6+2^4+2^3$

Answer: $2^{10}+2^9+2^8+2^7+2^6+2^4+2^3$