lecture08 - CMPT 150 Completeness Combinational Circuits...

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CMPT 150 Completeness & Combinational Circuits Page 1 Completeness b A set of Boolean functions is said to be complete if all other Boolean functions can be implemented from them. b Consider the Boolean functions AND, OR, and NOT. b Recall, for two variables, the functions we can have are: B A B F 0 F 1 F 2 F 3 F 4 F 5 F 6 F 7 F 8 F 9 F 10 F 11 F 12 F 13 F 14 F 15 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 b Can we implement F 0 and F 15 using AND, OR, and NOT? CMPT 150 Completeness & Combinational Circuits Page 2 Completeness b What about the rest of the functions? b Can use sum-of-products form, which uses AND, OR and NOT. b E.g. b Thus, the set of functions AND, OR, and NOT is complete. CMPT 150 Completeness & Combinational Circuits Page 3 Completeness b Question: Is NAND complete? CMPT 150 Completeness & Combinational Circuits Page 4 XOR with more inputs b Consider the following: x y z = And the truth table:
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This note was uploaded on 04/27/2011 for the course CMPT 150 taught by Professor Dr.anthonydixon during the Spring '08 term at Simon Fraser.

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lecture08 - CMPT 150 Completeness Combinational Circuits...

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