ECE 2000 Final Notes Sheet
ECE 2000 Final Notes Sheet
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This 4 page Study Guide was uploaded by Kyla Bouldin on Friday December 12, 2014. The Study Guide belongs to a course at a university taught by a professor in Fall. Since its upload, it has received 100 views.
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Date Created: 12/12/14
Number Systems Bases and Conversion 2562510 11OO11O12 252 12R1 625X2 1250 122 SRO 250X2 0500 62 3R0 500X2 100 32 1R1 12 0R1 Binary Addition 1 1 O carry 1 Binary Subtraction O 1 1 borrow 1 Signed Numbers SignMagnitude 4 0100 I 41100 139s Complement Flip the Bits 50101 I 51010 Addition add around any carry Overflow Detection if the two addends have the same sign but the sum has a different sign then there is overflow 239s Complement Flip the Bits and add 1 50101 I 51011 Addition ignore any carry Overflow Detection If carry into MSB is different than carry out of it then there is overflow Boolean Algebra X0X X1X X11 X00 XXX XXX XX1 XX0 Communicative XYYX XYYX Associative XYZ XYZ XYZ XYZ Distributive XYZ XYXZ XYZ XYXZ DeMorgans Theorem X Y X Y W X Y More Identities X XY X XY X X X XY X Y Duals XX Y X UmX XX Y XY Consensus Theorem XYXZYZ XYXZ mmmammmm Exclusive OR XEBY XY XY Standard Forms Truth Tables amp Kmaps Sum of Minterms Z m1237 Find 1s in truth table Product of Maxterms l39M0156 Find Os in truth table Sum of Products acbc Combine 139s in kmap Product of Sums Combine 039s complement terms xYxzwzwY gt X Yx Z V ZW Y 00 O1 11 10 00 mo m1 m3 m2 01 m4 lTl5 m7 m5 11 m12 m13 m15 m14 10 ms m9 D111 Who 39Don t Care s function outputs that are not important for the system39s correct operation Implicant a product term of the function in the SoP form Prime Implicant an implicant that is not contained in any larger implicant Essential Prime Implicant a prime implicant that contains a minterm not covered in any other prime implicant Minimization Procedure 1 Generate all prime implicants Pls of the function 2 Include all essential Pls 3 For remaining minterns not included in essential Pls select a set of Pls to cover them with minimal overlap in the set Sum of Products Example 00 O1 11 10 00 O1 11 10 Pls 5136 5651 ad bd Essential Pls BEE dbd F 13661 ad bd Gates Mapping to NAND and NOR gates 1 Replace all AND and OR gates with 11 W for NAND GATES W for NOR gates AK 2 After this conversion cancel out inverters or extend them to branches Repeat until there is at most 1 inverter between each driving input or driving NANDNOR gate and each output or NANDNOR gate it drives 3 Convert inverters to NANDNOR Gates 3 State Buffer E is the enable coming into the side of the buffer 10 1 Delays amp Hazards A hazard is eliminated by adding a nonessential PI to the minimal expression Adders An adder gets inputted a carry in xi yi and outputs a sum and carry out Decoders amp Encoders Decoders a device with n inputs and 2quot outputs such that only the output that corresponds to the information encoded in the ninput bits is active Given equation find minterms and connect them using the given gate style A1 A2 Do D1 D2 D3 0 1 O O O 1 O 1 O O O O O 1 0 1 0 O O 1 l l Decoders with Enable are only active when EN 1 Encoders maps 2quot inputs to n outputs Reverse operation of a decoder Once all of the outputs have its combinations all other input combinations are quotdon39t care conditions D3 D2 D1 Do A1 Au 0 O O 1 O 0 0 0 1 O O 1 O 1 O O 1 0 1 O 0 0 1 1 MUX amp DEMUX Multiplexers MUX Acts like a switch that selects one of the data inputs and transmits it to the output Choose inputs to be select lines remaining input feeds data lines as identical inverse O or 1 Implementing functions with MUX A B c D F 0 0 0 0 0 0 0 0 1 1 C 0 0 1 0 0 B S1 O 0 1 1 1 A 52 0 1 0 0 1 0 1 0 1 0 0 1 1 0 0 D 0 0 1 1 1 0 D1 Y F 1 0 0 0 0 D2 1 0 0 1 0 D3 1 0 1 0 0 D 1 0 1 1 1 Vcc D5 1 1 0 0 1 LE D6 1 1 0 1 1 1 1 1 0 1 D7 1 1 1 1 1 Demultiplexer DEMUX Reverse operation of MUX N inputs as controls enable and 2quot output This is also a decoder with an enable input Si S0 D9 D1 D2 D3 l l l l QQOITI QOITIO OITIOQ ITIOQO
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