 Binary addition in logarithmic space

For canonical positive binary numeral system inputs, a logspace transducer can emit the canonical representation of their sum most significant digit first. Count the operand lengths, compute the final arithmetic carry to determine output length, and then compute each requested result digit by restarting the least-significant-first column recurrence. Each pass uses only a fixed number of $O(\log n)$-bit indices and one arithmetic carry. The binary-addition carry invariant proves correctness. Logspace composition by recomputation consequently permits any L property of the resulting digit string, including being a binary palindrome, to be tested without storing the sum.