Binary Notation/Examples/127

Example of Binary Notation

The number written in decimal notation as $127$ is expressed in binary notation as $1111111_2$.


Proof

\(\ds 127\) \(=\) \(\ds 1 \times 2^6 + 1 \times 2^5 + 1 \times 2^4 + 1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0\)
\(\ds \) \(=\) \(\ds 64 + 32 + 16 + 8 + 4 + 2 + 1\)
\(\ds \) \(=\) \(\ds 1111111_2\)

$\blacksquare$


Sources

  • 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {1-2}$ The Basis Representation Theorem: Exercise $2$
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