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- W3100631062 abstract "The depth-optimal and (size + depth)-optimal circuits described in Chapters 5 and 6 have the property that they have a constant or fixed fan-in but unbounded fan-out. From practical considerations, it is desirable to construct circuits with bounded fan-out as well. In this Chapter, we first describe general methods for bounding fan-out in circuits, and then demonstrate an application of these techniques to obtain parallel prefix circuits with fixed fan-in and fixed fan-out. However, bounding fan-out increases the size and depth. The principal result of this Chapter is to derive bounds on the increase in the size and depth resulting from fixing the fan-out. A glance at the structure of the d-optimal and (s, d)-optimal circuits defined in Chapters 5 and 6 reveals that these circuits have unbounded fan-out (that is, fan-out is a function of N, the number of inputs). However, in practice, such as, in VLSI implementation, for practical reasons stemming from power, noise, and reliability considerations, the fan-out has to be limited to a small, fixed number, for instance, k (such as 2 or 3). We first describe an optimal method for bounding fan-out and then apply it to prefix circuits. To understand the effect of limiting the fan-out, consider an example of a node a in Figure 1, with fan-out 9. This can be thought of as a 9-ary tree with a as its root, and bi, 1 ≤ i ≤ 9 as the leaves. Suppose that we have to limit the fan-out to 3. That is, we have to replace the 9- ary tree in Figure 1 by a 3-ary tree with a as its root and bi, 1 ≤ i ≤ 9, as the leaves with the constraint that the values of the leaves remain unchanged. One such tree is given in Figure 2. Clearly, restricting the fan-out simultaneously increases the depth and the size of the circuit. In this example, the size is increased by 3 and the depth by 1." @default.
- W3100631062 created "2020-11-23" @default.
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- W3100631062 creator A5048317896 @default.
- W3100631062 date "1994-09-08" @default.
- W3100631062 modified "2023-09-26" @default.
- W3100631062 title "Bounding Fan-Out In Parallel Prefix Circuits" @default.
- W3100631062 doi "https://doi.org/10.1093/oso/9780195088496.003.0015" @default.
- W3100631062 hasPublicationYear "1994" @default.
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