l14_ece15a_prn

l14_ece15a_prn - ECE 15A Fundamentals of Logic Design...

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1 ECE 15A Fundamentals of Logic Design Lecture 14 Malgorzata Marek-Sadowska Electrical and Computer Engineering Department UCSB 2 Today: Overview ± Multi-level circuits, conversion of forms ± Quine-McCluskey simplification ± Petrick’s method ± Propagation delays/circuit hazards ± MUX as circuit element ± Mux expansion ± 3-state buffers
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2 3 Multi-level circuit realizations – conversion of forms ± Draw the circuit for the following Boolean algebraic expression F=((x+y)w’+z)XOR(x’y+z’) z Show a NOR-NOR realization for F. x y w z 4 Multi-level circuit realizations – conversion of forms ± F=((x+y)w’+z)XOR(x’y+z’) z Show a NOR-NOR realization for F. x y w z a b b a XOR a b f 0 0 0 0 1 1 1 0 1 1 1 0
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3 5 Multi-level circuit realizations – conversion of forms ± F=((x+y)w’+z)XOR(x’y+z’) z Show a NOR-NOR realization for F. x y w z 6 Multi-level circuit realizations – conversion of forms ± F=((x+y)w’+z)XOR(x’y+z’) z Show a NOR-NOR realization for F. x y w z
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4 7 Multi-level circuit realizations – conversion of forms ± F=((x+y)w’+z)XOR(x’y+z’) z Show a NOR-NOR realization for F. x y w z 8 Multi-level circuit realizations – conversion of forms ± F=((x+y)w’+z)XOR(x’y+z’) z Show a NOR-NOR realization for F. x y w z
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5 9 Multi-level circuit realizations – conversion of forms ± F=((x+y)w’+z)XOR(x’y+z’) z Show a NOR-NOR realization for F. x y w z 10 Quine-McCluskey Method 1. Construct the Implicant Table a) Group minterms by number of 1’s b) Apply Adjacency Theorem to pairs of implicants c) Mark all implicants that are used in larger groups
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6 11 Notation F(A, B, C, D) = Σ m(4,5,6,8,10,11) 1 ABCD 4 0100 ABCD 8 1000 2 ABCD 5 0101 ABCD 6 0110 ABCD 10 1010 3A B C D 1 1 1 0 1 1 Full variable decimal 1,0,- 12 Example ± Simplify F(a,b,c,d)= a’b’c’+a’b’cd’+a’bd+bcd’+ab’c’+ab’cd’ using Quine-McCluskey method.
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7 13 Quine-McCluskey Method Example group 0 group 1 group 2 group 3 0 0000 1 0001 2 0010 8 1000 5 0101 6 0110 9 1001 10 1010 7 0111 14 1110 Column I Column II Combine group 0 and group 1: = ) 14 , 10 , 9 , 8 , 7 , 6 , 5 , 2 , 1 , 0 ( m F 14 Example (cont.) group 0 group 1 group 2 group 3 0 0000 1 0001 2 0010 8 1000 5 0101 6 0110 9 1001 10 1010 7 0111 14 1110 Column I Column II 0,1 000- 0,2 00-0 0,8 -000 Combine group 1 and group 2.
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8 15 Example (cont.) group 0 group 1 group 2 group 3 0 0000 1 0001 2 0010 8 1000 5 0101 6 0110 9 1001 10 1010 7 0111 14 1110 Column I Column II 0,1 000- 0,2 00-0 0,8 -000 1,5 0-01 1,9 -001 2,6 0-10 2,10 -010 8,9 100- 8,10 10-0 Combine group 2 and group 3.
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l14_ece15a_prn - ECE 15A Fundamentals of Logic Design...

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