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Chapter 07 - Multilevel Logic-2x2(1)

# Chapter 07 - Multilevel Logic-2x2(1) - Multi-Level Gate...

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(-&59*7 ' 3:29/±2*;*2 ,&9* (/7(:/98 4&4) &4) 4²7 ,&9*8 Click the mouse to move to the next page± Use the ESC key to exit this chapter± ±²³ Multi´Level ,ate (ircuits ±²µ N&N) and NOR ,ates ±²¶ )esign of Two´Level (ircuits Using N&N)s and NORs ±²· )esign of Multi´Level N&N) and NOR ,ate (ircuits ±²¸ (ircuit (onversion Using &lternative ,ate Symbols ±²¹ )esign of Two´Levelº Multiple´Output (ircuits ±²± Multiple´Output N&N) and NOR (ircuits .n this unitº we will use the following terminology» ±² AND³OR circuit means a two´level circuit composed of a level of &N) gates followed by an OR gate at the output² ´² OR³AND circuit means a two´level circuit composed of a level of OR gates followed by an &N) gate at the output² µ² OR³AND³OR circuit means a three´level circuit composed of a level of OR gates followed by a level of &N) gates followed by an OR gate at the output² ¶² (ircuit of &N) and OR gates implies no particular ordering of the gates the output gate may be either &N) or OR² Multi±Level Gate Circuits Tree Diagrams *ach node on a tree diagram represents a gateº and the number of gate inputs is written beside each node² )UMa^K '±! ± Four²Level Realization of D )UMa^K '±!* Four²Level Realization of Z

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)UMa^K '±"* Three±Level Realization of Z Example Section ±²³ ´p² ³µ³¶ +ind a circuit of &N) and OR gates to realize (onsider solutions with two levels of gates and three levels of gates± Try to minimize the number of gates and the total number of gate inputs± &ssume that all variables and their complements are available as inputs± +irst² simplify I by using a Karnaugh map± I ³ a± b± c± d ´ " ū m ³µ² ¶² ·² µ¸² µ¹² µº´ )UMa^K '±# )UMa^K '±\$ This leads directly to a two»level &N)» OR gate circuit±
)UMa^K '±% +actoring yields I " c′d ± a ʓ ± b ² ³ cd ʓ ± a ± b ² 'oth of these solutions have an OR gate at the output´ & solution with an &N) gate at the output might have fewer gates or gate inputs´ & twoµlevel ORµ&N) circuit corresponds to a productµofµsums expression for the function´ This can be obtained from the ¶′s on the Karnaugh map as follows· *quation ±¸µ¹² leads directly to a twoµlevel ORµ&N) circuit´ I ʓ " c′d ³ ab′c′ ± cd ± a′b′c ±¸µº² I " ± c ± d ²± a ʓ ± b ± c ²± c ʓ ± d ʓ ²± a ± b ± c ʓ ² ±¸µ¹² )UMa^K '±& Section ±²³ ´p² ³µ¶·

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