4-Bit Ripple-Carry Adder

A ripple-carry adder is the most direct way to add multi-bit numbers: line up one full adder per bit and connect them by their carry signals. The lowest full adder takes a carry-in of 0. Each higher adder takes its carry-in from the carry-out of the adder just below it.

The name describes the behavior. The carry "ripples" from bit 0 upward: bit 1 cannot finish until bit 0's carry is known, bit 2 waits on bit 1, and so on. The carry-out of the top bit tells you whether the result overflowed the width you allotted — if your sum output is only four bits, a set top carry means the true answer needed a fifth bit.

The most common mistake is mis-chaining the carries — for example, feeding bit 2's carry-in from bit 0 instead of bit 1. The low bit stays correct, so the design looks almost right, but the middle bits compute with a stale carry and specific rows fail. Tracing the carry from bit 0 upward is the fastest way to find the broken link.