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 CHAPTER 11 Foundations of Combinational Circuits

In this chapter, we define and study combinational circuits. The underlying graph of a combinational circuit is more general than the underlying graph of a Boolean formula. In a formula, the underlying graph is a rooted tree. However, in a combinational circuit, the underlying graph is a directed acyclic graph.

We focus on the representation of Boolean functions by combinational circuits, a representation that is different from tables and formulas. Our goal is to prove two theorems: (i) every Boolean function can be implemented by a combinational circuit and (ii) every combinational circuit implements a Boolean function.

We introduce an efficient algorithm for simulating a combinational ...

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