Restructered pre-import

Old Pages/Old Wiki/Discussion_2_Exercises_Solution_notes.md

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+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 using only the three components
+listed above?
+
+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
+
+alpha=!(A+B) beta=!(alpha+A) gamma=!(alpha+!B) OUT=!(beta+gama)
+
+OUT=!(!(alpha+A) + !(alpha+!B)) substitution OUT=!(!(!(A+B)+A) +
+!(!(A+B)+!B)) substitution OUT=!(!(!A\*!B+A) + !(!A\*!B+!B)) demorgans
+OUT=!!(!A\*!B+A) \* !!(!A\*!B+!B) demorgans OUT= (!A\*!B+A) \*
+(!A\*!B+!B) identity 4 elementary OUT= (!A\*!B+A) \* (!B) identity 10
+absorption OUT= (!A\*!B+A\*!B) identity 8 distributivity OUT= !B (!A +
+A) identity 8 distributivity OUT= !B 5 elementary
+
+Since this can be implemented with a single inverter, the smallest
+propagation delays is 1ns.
+
+[Category:FPGAWorkshop](Category:FPGAWorkshop "wikilink")