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# TI 84 Plus: Expressing an Integer as a Sum of Powers of Two

TI 84 Plus:  Expressing an Integer as a Sum of Powers of Two

Happy Thanksgiving!

The program POW2SUM expresses a positive integer as a sum of powers of 2.  The program generates a list of terms.

The powers of 2 are:

2^0 = 1
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64
and so on.

Examples:

117 = 1 + 4 + 16 + 32 + 64 (+ 0)
(117 = 2^0 + 2^2 + 2^4 + 2^6)

386 = 2 + 128 + 256
(386 = 2^1 + 2^7 + 2^8)

Note:  The list includes a 0 (due to programming limitations on the TI-84 Plus).

TI 84 Plus Program POW2SUM

“EWS 2018-11-18”
Disp “N = 2^P1+2^P2+…”
Prompt N
{0} → L₁
Repeat N≤0
ln(N)/ln(2) → P
iPart(P) → P
N-2^P → N
augment({2^P},L₁) → L₁
End
Pause L₁

(I like Unicode)

Eddie

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