04 Combinational Logic Circuit Design

04 Combinational Logic Circuit Design - EE2000 Logic...

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1 EE2000 Logic Circuit Design 4 Combinational Logic Circuit Design ±±±
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2 Outline ± 4.1 Design Procedure ± 4.2 Design Examples ± Staircase Lighting Circuit ± Code Converter Circuit ± Seven-Segment Display Circuit ± 4.3 Design Issues ± Timing Hazard
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3 4.1 Design Procedure ± 1) Specification ± Write a specification for the circuit ± 2) Formulation ± Derive the truth table (or initial Boolean equations) to define the relationships between inputs and outputs ± 3) Optimization ± Apply logic circuit optimization ± 4) Technology Mapping ± Transform logic diagram to a new diagram using available implementation technology ± 5) Verification ± Verify the correctness of the final design
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4 4.2 Design Examples
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5 4.2.1 Staircase Lighting Circuit On/Off Button A On/Off Button B On/Off Button A On/Off Button B = On/Off Button A On/Off Button B = On/Off Button A On/Off Button B = On/Off Button A On/Off Button B =
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6 4.2.1 Staircase Lighting Circuit ± Specification: ± Design of a staircase lighting circuit ± There are two input buttons namely A & B ± The bulb will light on if both buttons have been turned up or down. It will light off if one button is up and the other one is down On/Off Button A On/Off Button B ? A B F
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7 Formulation ± Derive the truth table relating input and output variables from specification ± Optimization: ± From the truth table, ± F ( A , B ) = AB + A’B’ (= A B) Inputs Output A B F 0 0 1 0 1 0 1 0 0 1 1 1 F ( A , B ) is 1 if (A = 0 AND B = 0) OR (A = 1 AND B = 1) i.e. F ( A , B ) = A’B’ + AB = Σ m (0, 3)
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8 The Final Logic Diagram A B F = A’B’ + AB On/Off Button A On/Off Button B ? A B F A B F = A B
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9 4.2.2 Code Converter Circuit ± Specification: ± Design of a BCD-to-Excess-3 Code Converter ± XS3 code for a decimal digit is the binary combination corresponding to the decimal digit plus 3 ± Each BCD digit labeled from MSB, A , B , C , D ± The XS3 digit labeled from MSB, W , X , Y , Z ± i.e. ( ABCD ) BCD = ( WXYZ ) XS3
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10 The Rough Picture ± Design a logic circuit that perform code conversion ± Input is BCD 8421 code ± Output is Excess-3 code A B C W X Y Z D Excess-3 code BCD code ? (MSB) (LSB) (MSB) (LSB)
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11 Formulation Decimal digit Input (BCD 8421 Code) Output (Excess-3 Code) A B C D W X Y Z 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 2 0 0 1 0 0 1 0 1 3 0 0 1 1 0 1 1 0 4 0 1 0 0 0 1 1 1 5 0 1 0 1 1 0 0 0 6 0 1 1 0 1 0 0 1 7 0 1 1 1 1 0 1 0 8 1 0 0 0 1 0 1 1 9 1 0 0 1 1 1 0 0 Unused 1 0 1 0 x x x x Unused 1 0 1 1 x x x x unused 1 1 0 0 x x x x Unused 1 1 0 1 x x x x Unused 1 1 1 0 x x x x Unused 1 1 1 1 x x x x Some input combinations are illegal as they are no meaning in BCD code. We can treat the corresponding outputs as don’t care
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Optimization ± There are four variables ( A , B , C , D ) in the functions ± Each output variable depends on 4 variables ± So we need 4 four-variable K-maps ± W ( A , B , C , D ) = Σ m (5, 6, 7, 8, 9) + Σ d (10, 11, 12, 13, 14, 15) ± X ( A , B , C , D ) = Σ m (1, 2, 3, 4, 9) + Σ d (10, 11, 12, 13, 14, 15) ± Y ( A , B , C , D ) = Σ m (0, 3, 4, 7, 8) +
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04 Combinational Logic Circuit Design - EE2000 Logic...

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