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Chapter 2

Combinational Design Examples

In chapter 1 we have brieﬂy seen how to use most of the tools in Alliance. In this chapter we will explain

the design of combinational circuits. We will provide some examples and explain them. We will start with a

bottom-up built circuit. This style could be useful when designing more complex circuits.

2.1 The design of a 4-bit multiplier using adder trees

Here we will explain the design of a basic 4-bit multiplier circuit. A multiplier can be built using the three

blocks shown in Figure 2.1. The ﬁrst block producing the partial products can be implemented with very simple

Figure 2.1: The basic blocks to built.

circuitry as the one shown in Figure 2.2. For the adder trees we can use m any schemes. In Figure 2.3 we shown

Figure 2.2: 4-bit partial product generator.

three schemes. The ﬁrst one (most left) is the one of Wallace[1]. The one in the middle is due to Dadda[2], and

the one on the right is of reference[3]. We will design the multiplier of this s ec tion using these three schemes and

compare the areas of the circuits obtained with them. Wallace is the method more frequently used in research

and commercial designs. Dadda’s tree is an optional method that produces smaller designs. The third one is

another way of structuring the adder in the tree. With this method we reduce the number of half adders in the

tree and the number of bits to the ﬁnal adder. The rectangular blocks in the trees represent the half adder and

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ADDER X-SC Manual do Utilizador Página 59