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## E.2    MULTIPLEXER-BASED FAST BINARY ADDERS

This section considers implementation of Manchester, carry-select, and carry- look-ahead based fast binary adders using multiplexers only.

Fig. E.1    Block diagram of a Manchester adder.

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 [1]. 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:

• PG-logic: compute all pairs of (gi, pi) based on (E.1) and (E.2) in parallel;
• Carry-generator: computes all carries ci+1 based on (E.3);
• Sum-generator: computes all sum bits

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