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Where the a^b means a raised to the b power:
1111111 = 2^6 + 2^5 + 2^4 + 2^3 + 2^2 + 2^1 + 2^0 = 64 + 32 + 16 + 8 + 4 + 2 + 1 = 127
or
Add 1 to reduce the number of 1's to process: 1111111 + 1 = 10000000 = 2^7 = 128

Subtract 1 to get back to the original number: 10000000 - 1 = 128 - 1 = 1111111 = 127

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