This does not match your criteria, but feels similar. It is a method for multiplying two decimals, say $13 \times 27$. Form two columns headed by $13$ and $27$. Halve $13$ and discard any remainder, and double $27$. Continue halving the first column and doubling the second until the first column reaches $1$:

\begin{array} \mbox{13} & 27 \\ {\color{red}{6}} & {\color{red}{54}} \\ 3 & 108 \\ 1 & 216 \end{array}

Now discard any row for which the first column is even ($\color{red}{6}$ above). Sum the remaining elements of the second column: $$27 + 108 + 216 = 351 = 13 \times 27 \;.$$ This is of course using the binary representation $13 = 2^0 + 2^2 + 2^3$, and first including but later excluding the $2^1$ row $\color{red}{6} \;\; \color{red}{54}$.

This does not quite match your criteria, but feels similar. It is a method for multiplying two decimals, say $13 \times 27$. Form two columns headed by $13$ and $27$. Halve $13$ and discard any remainder, and double $27$. Continue halving the first column and doubling the second until the first column reaches $1$:

\begin{array} \mbox{13} & 27 \\ {\color{red}{6}} & {\color{red}{54}} \\ 3 & 108 \\ 1 & 216 \end{array}

Now discard any row for which the first column is even ($\color{red}{6}$ above). Sum the remaining elements of the second column: $$27 + 108 + 216 = 351 = 13 \times 27 \;.$$ This is of course using the binary representation $13 = 2^0 + 2^2 + 2^3$, and first including but later excluding the $2^1$ row $\color{red}{6} \;\; \color{red}{54}$.