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Consider a simple example of an addition X = A + B + C + D, where all the variables are digital words. We could implement this using adders, taking two numbers at a time and then adding the answer to the next input. This would give the data flow diagram shown in Figure 16.4.
This implementation requires three adders and takes three cycles to get the answer. If we were more systematic with the same resources, we could reduce this to two cycles by adopting a different structure, as shown in Figure 16.5.
Figure 16.5
Reduced cycle implementation.
This is a classic case of an expression tree being reduced so that the control path can take fewer cycles, but achieving the same data path result. We could also the envisage the case where we only use a single addition block, but use registers to store the intermediate sums and then pipeline the sums until we complete the expression. This would potentially take the longest, but would result in the smallest area requirement as there would only be the need for a single addition block (of course, this would be a trade-off with an increased number of registers).
Critical Path Analysis
Another approach to logic optimization is to analyze the critical path through a design from a timing perspective. This is often carried out automatically by the synthesis software; for example, the Synopsys© Design Compiler software automatically generates a synthesized schematic that highlights the critical path through the design for timing and as such designers can concentrate their efforts on that area of the design to improve the overall throughput in that case (see Figure 16.6)
Figure 16.6
Reduced cycle implementation.
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