How do Topological Properties of Ripple-Carry Adders Affect Time Delay?

This poster presents topological properties of N-bit ripple-carry adders and the effects of their topology, specifically their genus, on the speed of current flow. An adder is a very simple computer that takes input numbers (0 and 1) from logic gates and then adds them together. To create a ripple-carry adder, we take N number of adder circuits and arrange them in parallel. We differentiate between two kinds of adder circuits: half adders and full adders. Half adders are non-planar (has loops) circuits with genus = 1 that let us perform elementary addition operations using logic gates. Full adder circuits are non-planar circuits with genus = 2 that comprise three inputs (A, B, and the Carry input) and two outputs (Sum and the Carry output), sending the carry input from one adder to the next. We can think of the genus of a circuit as the number of loops a surface needs in order for a circuit to be drawn on it without any crossings.https://idun.augsburg.edu/zyzzogeton/1001/thumbnail.jp