Operational Trans conductance Amplifiers:Binary Decision Diagrams

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Binary Decision Diagrams

Truth tables or logic expressions can be expressed with binary decision diagrams, which are usually abbreviated as BDDs. Compared with logic expressions or truth tables, BDDs have unique features, such as unique concise representation, processing speed, and the memory space, as discussed in a later section.

Let us consider a logic expression, x1x2 ∨ x3 , for example. This can be expressed as the truth table shown in Figure 26.6(a). Then, this can be expressed as the BDD shown in Figure 26.6(b). It is easy to see why Figure 26.6(b) represents the truth table in Figure 26.6(a). Let us consider the row, (x1x2x3) = (011), for example, in Figure 26.6(a). In Figure 26.6(b), starting from the top node which represents x1, we go down to the left node which represents x2, following the dotted line corresponding to x1 = 0. From this node, we go down to the second node from the left which represents x3, following the solid line corresponding to x2 = 1. From this node, we go down to the fourth rectangle from the left which represents, f = 1, following the solid line corresponding to x3 = 1. Thus, we have the value of f that is shown for the row, (x1, x2, x3) = (011) in the truth table in Figure 26.6(a). Similarly, for any row in the truth table, we reach the rectangle that shows the value of f identical to that in the truth table in Figure 26.6(a), by following a solid or dotted line corresponding to 1 or 0 for each of x1, x2, x3, respectively. BDD in Figure 26.6(b) can be simplified to

Expressions of Logic Functions-0341

When a function has don’t-cares, d’s, we can treat it in the same manner by considering a rectangle for d’s, as shown in Figure 26.7.

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