https://wiki.hacdc.org/index.php?title=Discussion_2_Exercises_Solution_notes&feed=atom&action=historyDiscussion 2 Exercises Solution notes - Revision history2022-11-29T21:09:49ZRevision history for this page on the wikiMediaWiki 1.37.1https://wiki.hacdc.org/index.php?title=Discussion_2_Exercises_Solution_notes&diff=2390&oldid=prevWilliamgibb: Created page with 'Problem 4, Part D was omitted from the solutions. It is presented here. D) What is t_pd of the fastest equivalent circuit (i.e. one that implements the same function) built usi…'2009-10-25T05:58:36Z<p>Created page with 'Problem 4, Part D was omitted from the solutions. It is presented here. D) What is t_pd of the fastest equivalent circuit (i.e. one that implements the same function) built usi…'</p>
<p><b>New page</b></p><div>Problem 4, Part D was omitted from the solutions. It is presented here.<br />
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D) What is t_pd of the fastest equivalent circuit (i.e. one that implements the same function) built using only the three components listed above?<br />
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Lets start by reducing the logic equation....I'm going to use three intermediary signals, alpha, beta and gamma, and pull identity numbers from the slides<br />
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alpha=!(A+B)<br />
beta=!(alpha+A)<br />
gamma=!(alpha+!B)<br />
OUT=!(beta+gama)<br />
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OUT=!(!(alpha+A) + !(alpha+!B)) substitution<br />
OUT=!(!(!(A+B)+A) + !(!(A+B)+!B)) substitution<br />
OUT=!(!(!A*!B+A) + !(!A*!B+!B)) demorgans<br />
OUT=!!(!A*!B+A) * !!(!A*!B+!B) demorgans<br />
OUT= (!A*!B+A) * (!A*!B+!B) identity 4 elementary<br />
OUT= (!A*!B+A) * (!B) identity 10 absorption<br />
OUT= (!A*!B+A*!B) identity 8 distributivity<br />
OUT= !B (!A + A) identity 8 distributivity<br />
OUT= !B 5 elementary<br />
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Since this can be implemented with a single inverter, the smallest propagation delays is 1ns.<br />
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[[Category:FPGAWorkshop]]</div>Williamgibb