Technology Mapping for LUT-Based FPGA by Marcin Kubica & Adam Opara & Dariusz Kania

Author:Marcin Kubica & Adam Opara & Dariusz Kania
Language: eng
Format: epub
ISBN: 9783030604882
Publisher: Springer International Publishing

(8.2)

More advanced exemplary representations of a PMTBDD diagram for the multioutput function f0f1f2 is presented in Fig. 8.11. In each case the leaf of an MTBDD diagram placed on the left corresponds to the PMTBDD representation placed on the right. For example, the leaf 111f0,f1,f2, correlates with a subdiagram of the form [2].

Fig. 8.11Examples of representations of leaves in the diagrams MTBDD and PMTBDD for a multioutput function f0, f1, f2. (see Footnote 1) [2]

Replacing MTBDD leaves with nonterminal nodes gives the possibility of processing the entire diagram using the same procedure. Thus, a separate procedure to process MTBDD leaves is not needed. By appropriately specifying the expressions that describe subdiagrams that replace MTBDD leaves (expression 8.1), merging several diagrams into the diagram of multioutput function may be performed using a standard OR operation (see Footnote 1) [2].

The process of merging ROBDD diagrams into one PMTBDD will be presented using the example of the function f0 =  x0 + x1, f1 =  x0· x1. With two ROBDD diagrams for f0 and f1 (Fig. 8.12), additional variables f0′, should be introduced and appropriate additional variable should be multiplied by a function. After multiplying, the expressions p0 = ·(x0 +  x1) and p1 = · x0· x1, whose diagrams are presented in Fig. 8.12c, d, will be created. PMTBDD diagrams, similar to MTBDD diagrams, in special cases may represent single functions. To simplify the presented example, PMTBDD diagrams present a possibility in Fig. 8.12c, d. Each of the two PMTBDD diagrams represent a multioutput function; however, only one function exists in each multioutput function. All nodes below the nodes related to x1 are treated as MTBDD leaves. Because there is only one single output function, below level x1 only one level of nodes related to additionally introduced variables may exist (see Footnote 1) [2].

Fig. 8.12Process of transforming the diagrams: a, b ROBDD, c, d PMTBDD (see Footnote 1) [2]

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