Prove and explain how to represent 2n - 1 in binary notation

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Prove and explain how to represent 2n - 1 in binary notation

Prove and explain how to represent 2ⁿ - 1 in binary notation

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Answer 1

Answer #1

2^n - 1

if n is 1, then 2^1 - 1 = 2 - 1 = 1. it's binary form is 1
if n is 2, then 2^2 - 1 = 4 - 1 = 3. it's binary form is 11
if n is 3, then 2^3 - 1 = 8 - 1 = 7. it's binary form is 111
so, 2^n - 1 in binary form is 111...1 => (n 1's)

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Answer 2

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