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ECE 331 – Digital System Design

ECE 331 – Digital System Design. Logic Circuit Design (Lecture #7). Design Concepts. Combinational Logic Circuits Outputs are functions of (present) inputs No memory Can be described using Boolean expressions Hierarchical design Used to solve large design problems

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ECE 331 – Digital System Design

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  1. ECE 331 – Digital System Design Logic Circuit Design (Lecture #7)

  2. ECE 331 - Digital System Design Design Concepts Combinational Logic Circuits Outputs are functions of (present) inputs No memory Can be described using Boolean expressions Hierarchical design Used to solve large design problems Break problem into smaller (sub-)problems Solve each sub-problem (i.e. realize design) Combine individual solutions

  3. ECE 331 - Digital System Design Design Concepts Specification Describes the problem to be solved. Describes what needs to be done, not how to do it. Implementation Describes how the problem is solved.

  4. ECE 331 - Digital System Design Design Concepts Issues Most solutions are not unique. More than one solution may meet the specifications. Cannot always satisfy all of the requirements. Must identify (and study) design tradeoffs. Cost Speed Power consumption etc.

  5. ECE 331 - Digital System Design Design Process Identify requirements (i.e. circuit specifications) Determine the inputs and outputs. Derive the Truth Table Determine simplified Boolean expression(s) Implement solution Verify solution

  6. ECE 331 - Digital System Design Exercise: Design a combinational logic circuit to meet the following specifications: 1. 3-bit input (A = a2a1a0) 2. 1-bit output (z) 3. Output is high (logic 1) when 2 < A <= 5.

  7. ECE 331 - Digital System Design Example: Design a 7-Segment Decoder

  8. ECE 331 - Digital System Design 1. Circuit Specification The 7-Segment Decoder must decode Binary Coded Decimal (BCD) digits so that they can be displayed on a 7-Segment Display. 7-Segment Decoder

  9. ECE 331 - Digital System Design 2. Determine Inputs and Outputs Input: Binary Coded Decimal digits 7-Segment Decoder

  10. ECE 331 - Digital System Design Binary Coded Decimal Assign a 4-bit code to each decimal digit. A 4-bit code can represent 16 values. There are only 10 digits in the decimal number system. Unassigned codes are not used. How do we interpret these unused codes? Hint: think about K-maps.

  11. ECE 331 - Digital System Design BCD Digits

  12. ECE 331 - Digital System Design 2. Determine Inputs and Outputs Output: 7-Segment Display 7-Segment Decoder

  13. ECE 331 - Digital System Design 7-Segment Display

  14. ECE 331 - Digital System Design 7-Segment Display

  15. ECE 331 - Digital System Design 3. Derive Truth Table 7-Segment Decoder

  16. ECE 331 - Digital System Design 7-Segment Decoder

  17. ECE 331 - Digital System Design 4. Determine simplified Boolean expression(s) 7-Segment Decoder

  18. ECE 331 - Digital System Design 7-Segment Decoder A y z w x 00 01 11 10 00 1 0 1 1 01 0 1 1 1 11 d d d d 10 1 1 d d A = ?

  19. ECE 331 - Digital System Design 7-Segment Decoder B y z w x 00 01 11 10 00 1 1 1 1 01 1 0 1 0 11 d d d d 10 1 1 d d B = ?

  20. ECE 331 - Digital System Design Student Exercise: Determine the minimized Boolean expression for each of the segments of the 7-Segment Display. 7-Segment Decoder

  21. ECE 331 - Digital System Design 5. Implement Solution 6. Verify Solution 7-Segment Decoder

  22. ECE 331 - Digital System Design Multiple-Output Logic Circuits

  23. ECE 331 - Digital System Design Example: Given two functions, F1 and F2, of the same input variables x1.. x4, design the minimum-cost implementation. Multiple-Output Logic Circuits

  24. ECE 331 - Digital System Design Multiple-Output Logic Circuits x x x x 1 2 1 2 x x x x 3 4 3 4 00 01 11 10 00 01 11 10 00 1 1 00 1 1 01 1 1 1 01 1 1 11 1 1 11 1 1 1 10 1 1 10 1 1 (a) Function f (b) Function f 1 2 F1 = X1'.X3 + X1.X3' + X2.X3'.X4 F1 = X1'.X3 + X1.X3' + X2.X3.X4

  25. ECE 331 - Digital System Design Multiple-Output Logic Circuits x 2 x 3 x 4 f 1 x 1 x 3 x 1 x 3 f 2 x 2 x 3 x 4 f f (c) Combined circuit for and 1 2

  26. ECE 331 - Digital System Design Example: Given two functions, F3 and F4, of the same input variables x1.. x4, design the minimum-cost implementation for the combined circuit. Multiple-Output Logic Circuits Note: the minimum-cost implementation for the combined circuit may not be the same as the minimum-cost implementations for the individual circuits.

  27. ECE 331 - Digital System Design Multiple-Output Logic Circuits x x x x 1 2 1 2 x x x x 3 4 3 4 00 01 11 10 00 01 11 10 00 00 01 1 1 1 01 1 1 1 11 1 1 1 11 1 1 1 10 1 10 1 (a) Optimal realization of (b) Optimal realization of f f 3 4 F3 = X1'.X4 + X2.X4 + X1'.X2.X3 F3 = X2'.X4 + X1.X4 + X1'.X2.X3.X4' Logic Gates required: 2 2-input AND 1 3-input AND 1 3-input OR Logic Gates required: 2 2-input AND 1 4-input AND 1 3-input OR Total Gates and Inputs required: 8 Logic Gates 21 Inputs

  28. ECE 331 - Digital System Design Multiple-Output Logic Circuits x x x x 1 2 1 2 x x x x 3 4 3 4 00 01 11 10 00 01 11 10 00 00 01 1 1 1 01 1 1 1 11 1 1 1 11 1 1 1 10 1 10 1 (c) Optimal realization of f and f together 3 4 F3 = X1'.X4 + X1.X2.X4 + X1'.X2.X3.X4' F3 = X2'.X4 + X1.X2.X4 + X1'.X2.X3.X4' Logic Gates required: 1 2-input AND 1 3-input AND 1 4-input AND 1 3-input OR Logic Gates required: 1 2-input AND 1 3-input AND 1 4-input AND 1 3-input OR shared logic gates Total Gates and Inputs required: 6 Logic Gates 17 Inputs

  29. ECE 331 - Digital System Design Multiple-Output Logic Circuit x 1 x 4 x f 1 3 x 2 x 4 x 1 x 2 x 3 x f 4 4 x 2 x 4 f f (d) Combined circuit for and 3 4

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