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Designing Multi-Level Networks with Limited Gate Fan-in Using NOR and NAND Gates

This document discusses the design of multi-level networks constrained by limited gate fan-in. It explains the necessity of factoring logic expressions when the required number of gate inputs exceeds the allowed limit, using practical examples. One key focus is on realizing functions with three-input NOR gates, emphasizing the factoring techniques to reduce gate inputs. The document also outlines strategies for optimizing multiple-output networks by minimizing functions separately and introduces techniques like common term extraction for simplification. Practical applications demonstrate the conversion to appropriate gate forms.

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Designing Multi-Level Networks with Limited Gate Fan-in Using NOR and NAND Gates

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  1. Design of Networks with Limited Gate Fan-in If a two-level network realization requires more more gate Inputs than allowed, factoring the logic expression to obtain a multi-level realization is necessary. Example: Realize f(a,b,c,d) =S m(0,3,4,5,8,910,14,15) using three-input NOR gates. Soln.: -must use three-input NOR gates so factor expression for f’ and complement

  2. Design of Networks with Limited Gate Fan-in When designing multiple-output networks with more than two levels, it is usually best to minimize each function separately. -- resulting two-level expressions are factored to increase number of levels -- factoring should be done in a way that introduces common terms. Example: Realize the given functions using only two-input NAND gates and inverters. Soln.: -functions to be realized and k-maps are shown

  3. Design of Networks with Limited Gate Fan-in Example(cont’d): Realize the given functions using only two-input NAND gates and inverters. Soln.(cont’d): If we minimize each function separately the result is Factoring to reduce no. of gate inputs (while increasing no. of levels) Expression has common term -- preferred - common terms are underlined in the above expressions -the remaining 3-input gate in the f3 expression for can be eliminated using

  4. Design of Networks with Limited Gate Fan-in Example(cont’d): Realize the given functions using only two-input NAND gates and inverters. Soln.(cont’d): Realization converted to NAND form Realization

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