https://wiki.hacdc.org/index.php?title=Discussion_2_Exercises_Solution_notes&feed=atom&action=history Discussion 2 Exercises Solution notes - Revision history 2022-05-18T22:55:41Z Revision history for this page on the wiki MediaWiki 1.37.1 https://wiki.hacdc.org/index.php?title=Discussion_2_Exercises_Solution_notes&diff=2390&oldid=prev Williamgibb: 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 &#039;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…&#039;</p> <p><b>New page</b></p><div>Problem 4, Part D was omitted from the solutions. It is presented here.<br /> <br /> 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 /> <br /> Lets start by reducing the logic equation....I&#039;m going to use three intermediary signals, alpha, beta and gamma, and pull identity numbers from the slides<br /> <br /> alpha=!(A+B)<br /> beta=!(alpha+A)<br /> gamma=!(alpha+!B)<br /> OUT=!(beta+gama)<br /> <br /> 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 /> <br /> Since this can be implemented with a single inverter, the smallest propagation delays is 1ns.<br /> <br /> [[Category:FPGAWorkshop]]</div> Williamgibb