U of I CS 231 - Lecture notesl (31 pages)

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Lecture notesl



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Lecture notesl

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Lecture Notes


Pages:
31
School:
University of Illinois
Course:
Cs 231 - Fundamental Algorithms
Fundamental Algorithms Documents

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Additional gates We ve already seen all the basic Boolean operations and the associated primitive logic gates There are a few additional gates that are often used in logic design They are all equivalent to some combination of primitive gates But they have some interesting properties in their own right 01 14 19 Additional Gates and Decoders 1 Additional Boolean operations Operation Expressions Truth table NAND NOT AND xy x y x y xy 0 0 1 0 1 1 1 0 1 1 1 0 NOR NOT OR XOR eXclusive OR x y x y x y x y xy x y x y x y 0 0 1 0 0 x y 0 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 0 Logic gates 01 14 19 Additional Gates and Decoders 2 NANDs are special The NAND gate is universal it can replace all other gates NOT xx x because xx x xy xy xy from NOT above AND OR xx yy x y xx x and yy x y DeMorgan s law 01 14 19 Additional Gates and Decoders 3 Making NAND circuits The easiest way to make a NAND circuit is to start with a regular primitive gate based diagram Two level circuits are trivial to convert so here is a slightly more complex random example 01 14 19 Additional Gates and Decoders 4 Converting to a NAND circuit Step 1 Convert all AND gates to NAND gates using AND NOT symbols and convert all OR gates to NAND gates using NOT OR symbols 01 14 19 Additional Gates and Decoders 5 Converting to NAND concluded Step 2 Make sure you added bubbles along lines in pairs x x If not then either add inverters or complement the input variables 01 14 19 Additional Gates and Decoders 6 NOR gates The NOR operation is the dual of the NAND NOR gates are also universal We can convert arbitrary circuits to NOR diagrams by following a procedure similar to the one just shown Step 1 Convert all OR gates to NOR gates OR NOT and all AND gates to NOR gates NOT AND Step 2 Make sure that you added bubbles along lines in pairs If not then either add inverters or complement input variables 01 14 19 Additional Gates and Decoders 7 XOR gates A two input XOR gate outputs true when exactly one of its inputs is true x y



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