prelim1s - ENGRD 2300: Introduction to Digital Logic Design...

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ENGRD 2300: Introduction to Digital Logic Design Fall 2009 ENGRD 2300 – Fall 2009 Prelim 1 Solutions Problem 1. (25 points) Consider the following circuit. y x z a) Construct a CMOS circuit that is equivalent to the above circuit using the minimum possible number of transistors. Make sure that your CMOS circuit follows all the design rules for connecting PMOS and NMOS transistors! Partial credit will be given for any correctly formed equivalent circuit; full credit will only be given for correctly a formed circuit that uses the minimum possible number of transistors. For partial credit you can just draw the CMOS circuit for 4 NAND gates and connect them up as shown above. This solution requires 16 transistors. We can do better. (Max of 15 points for this solution.) You may have recognized this circuit from class as an XOR circuit. In any event, you can calculate that Z = X’·Y+X·Y’. Unfortunately there is no obvious way to implement this as a AND-OR-INVERT of OR-AND-INVERT. You can however implement the function (A·B + C·D)’ as an AND-OR-INVERT using 8 transistors. Using 4 more transistors to implement two NOT gates and using these NOT gates to produce X’ and Y’ and feeding X, X’,Y and Y’ into the AND-OR-INVERT appropriately (A=X, B=Y, C=X’, D=Y’) you can create a CMOS circuit that solves the problem using 12 transistors. (20 points for this solution.) 1
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ENGRD 2300: Introduction to Digital Logic Design Fall 2009 Alternatively, you can observe that Z = (X+Y)(X·Y)’. You can use a 4 transistor NAND circuit
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prelim1s - ENGRD 2300: Introduction to Digital Logic Design...

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