CEC 220 Digital Circuit Design NAND/NOR Multi-Level Circuits Wed, February 12 CEC 220 Digital Circuit Design

CEC 220 Digital Circuit Design Lecture Outline The Eight Basic Two-Level Circuits NAND/NOR Multi-Level Gate Circuits Design of Two-Level, Multiple-Output Circuits Multiple Output NAND/NOR Circuits Wed, February 12 CEC 220 Digital Circuit Design

NAND/NOR Multi-Level Circuits The Eight Basic Two-Level Circuits Assume that we are given the following K-Map(s) AB CD 00 01 11 10 1 AB CD 00 01 11 10 1 SOP POS Wed, February 12 CEC 220 Digital Circuit Design

NAND/NOR Multi-Level Circuits The Eight Basic Two-Level Circuits Two Level SOP Circuits AND OR NOR OR NAND NAND OR NAND Wed, February 12 CEC 220 Digital Circuit Design

NAND/NOR Multi-Level Circuits The Eight Basic Two-Level Circuits Two Level POS Circuits OR AND NAND AND NOR NOR AND NOR Wed, February 12 CEC 220 Digital Circuit Design

NAND/NOR Multi-Level Circuits NAND Multi-Level Gate Circuits Procedure for designing a minimum multi-level NAND-NAND circuit Find a minimum SOP expression for f. Draw the corresponding multi-level AND-OR circuit Replace all gates with NAND gates leaving the gate interconnections unchanged. Leave the inputs to levels 2,4,6, … unchanged. Invert any literals which appear as inputs to levels 1,3,5 … . Wed, February 12 CEC 220 Digital Circuit Design

NAND/NOR Multi-Level Circuits NAND Multi-Level Gate Circuits An Example AND & OR Network NAND-NAND network Wed, February 12 CEC 220 Digital Circuit Design

NAND/NOR Multi-Level Circuits NOR Multi-Level Gate Circuits Procedure for designing a minimum multi-level NOR-NOR circuit Find a minimum POS expression for f. Draw the corresponding multi-level OR-AND circuit Replace all gates with NOR gates leaving the gate interconnections unchanged. Leave the inputs to levels 2,4,6, … unchanged. Invert any literals which appear as inputs to levels 1,3,5 … . Wed, February 12 CEC 220 Digital Circuit Design

NAND/NOR Multi-Level Circuits NOR Multi-Level Gate Circuits An Example AND & OR Network NAND-NAND network Wed, February 12 CEC 220 Digital Circuit Design

CEC 220 Digital Circuit Design NAND/NOR Multi-Level Circuits Design of Two-Level, Multiple-Output Circuits AB CD 00 01 11 10 1 AB CD 00 01 11 10 1 AB CD 00 01 11 10 1 A total of 9 gates Wed, February 12 CEC 220 Digital Circuit Design

CEC 220 Digital Circuit Design NAND/NOR Multi-Level Circuits Design of Two-Level, Multiple-Output Circuits AB CD 00 01 11 10 1 AB CD 00 01 11 10 1 AB CD 00 01 11 10 1 A total of 7 gates Wed, February 12 CEC 220 Digital Circuit Design

NAND/NOR Multi-Level Circuits Examples Realize 𝑍=𝐴𝐵𝐶+𝐴𝐷+ 𝐶 𝐷 using as few 2-input NAND gates as possible Assume that the inputs and their inverses are both available AB CD 00 01 11 10 1 AB CD 00 01 11 10 Wed, February 12 CEC 220 Digital Circuit Design

NAND/NOR Multi-Level Circuits Examples A combinational switching circuit has four inputs (A,B,C,D) and one output (F). F=0 iff three or four of the inputs are 0. Write the maxterm expansion for F and implement using a minimum three level AND & OR gates. AB CD 00 01 11 10 AB CD 00 01 11 10 1 AB CD 00 01 11 10 Wed, February 12 CEC 220 Digital Circuit Design

NAND/NOR Multi-Level Circuits Examples Realize 𝑓= 𝑎 𝑏 +𝑎𝑏𝑑+𝑎𝑐𝑑 using a three or more level NOR-gate circuit. Wed, February 12 CEC 220 Digital Circuit Design

CEC 220 Digital Circuit Design Next Lecture Timing Diagrams Multiplexers Tri-State Buffers Wed, February 12 CEC 220 Digital Circuit Design