6301-7 - EE\/CE 6301 Advanced Digital Logic Bill Swartz Dept of EE Univ of Texas at Dallas EEDG\/CE6301 B Swartz 1 Session 07 Multi-Level Optimization

6301-7 - EE/CE 6301 Advanced Digital Logic Bill Swartz...

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1 EE/CE 6301: Advanced Digital Logic Bill Swartz Dept. of EE Univ. of Texas at Dallas EEDG/CE6301 B. Swartz
2 Multi-Level Optimization Session 07 Adapted from the work of M Nourani to whom I am grateful
3 Motivation for Multi-Level Optimization
4 General Form General circuits may have Sums within products Products within sums Arbitrary depth Example: z=((a . (b+c)+e) . f . g+h) . i
5 Example Two-Level vs. Multi-Level Consider the minimal 2-level SOP form # AND3 = 6; # OR7 = 1 Total = 7 gates # gate inputs = 25 This can be improved if we replace the 2-level form with a multi- level, factored form # AND3 = 1; # OR2 = 2; # OR3 = 1 Total = 4 gates! # gate inputs = 10 d e y Z f g a b c x f y d e x a b c g Z adf aef bdf bef cdf cef g  Z ad ae bd be cd ce f g Z a b c d a b c e f g Z a b c d e f g
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7 Multi-Level Optimization Methods
8 Fundamental Techniques Cubes Transformations Factorization Decomposition Extraction Substitution Collapsing Shannon Expansion Division Weak (Algebraic) Strong (Boolean)