When we write \(137\) in decimal, we mean \(1 \times 10^2 + 3 \times 10 + 7 \times 1\). If we write it instead using powers of \(2\), we have \(137 = 1 \times 2^7 + 0 \times 2^6 + 0 \times 2^5 + 0 \times 2^4 + 1 \times 2^3 + 0 \times 2^2 + 0 \times 2^1 + 1 \times 2^0\). To tell apart binary representation from decimals, we can use the following notation: \(137 = (10001001)_2\).
What is the number \(273\) in binary? Note that using binary is useful for finding whether a particular Nim game is a winning position or a losing position.