This section considers implementation of Manchester, carry-select, and carry- look-ahead based fast binary adders using multiplexers only.
In a binary addition, a carry ci can be either generated at stage i or propagated from the preceding stage. A carry is generated at stage i if xi and yi are both 1, and a carry is propagated from stage i−1 to stage i+1 if only one of the operands (xi, yi) is 1 but not both . Let gi and pi denote the carry generation and the propagation at stage i. These can be computed as:
where ⊕ denotes XOR operation. The carry ci+1 and the sum si at each stage are computed by:
Hence, an adder based on this principle consists of 3 sequential stages: