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

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About mvtrinh

Retired high school math teacher.
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