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Logic Circuit Design Concepts in Digital Electronics

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  1. Logic Circuit Design (Lecture #9) ECE 301 – Digital Electronics

  2. ECE 301 - Digital Electronics 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 301 - Digital Electronics 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 301 - Digital Electronics 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 301 - Digital Electronics 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 301 - Digital Electronics Example: Design a combinational logic circuit that compares two 2-bit numbers, A (a1a0) and B (b1b0), and outputs a 1 when A > B. Logic Circuit Design

  7. ECE 301 - Digital Electronics To implement the design, follow the 5 steps specified in the Design Process.

  8. ECE 301 - Digital Electronics Example: Design a combinational logic circuit to convert between Binary Coded Decimal (input) and Excess-3 Code (output) Logic Circuit Design

  9. ECE 301 - Digital Electronics 1. Circuit Specification The combinational logic circuit must convert a code value in Binary Coded Decimal to its corresponding code value in Excess-3 Code. Logic Circuit Design

  10. ECE 301 - Digital Electronics 2. Determine Inputs and Outputs Input: Binary Coded Decimal value Logic Circuit Design

  11. ECE 301 - Digital Electronics 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. • Remember “don't cares”?

  12. ECE 301 - Digital Electronics Binary Coded Decimal

  13. ECE 301 - Digital Electronics 2. Determine Inputs and Outputs Output: Excess-3 Code value Logic Circuit Design

  14. ECE 301 - Digital Electronics Excess-3 Code

  15. ECE 301 - Digital Electronics 3. Derive Truth Table Logic Circuit Design

  16. ECE 301 - Digital Electronics Code Conversion

  17. ECE 301 - Digital Electronics 4. Determine simplified Boolean expression(s) Logic Circuit Design

  18. ECE 301 - Digital Electronics Code Conversion

  19. ECE 301 - Digital Electronics Code Conversion

  20. ECE 301 - Digital Electronics Code Conversion

  21. ECE 301 - Digital Electronics Code Conversion

  22. ECE 301 - Digital Electronics 5. Implement Solution Logic Circuit Design

  23. ECE 301 - Digital Electronics Code Converter

  24. ECE 301 - Digital Electronics 6. Verify Solution (Analyze, Simulate, or Test the Logic Circuit) Logic Circuit Design

  25. ECE 301 - Digital Electronics Multiple-Output Logic Circuits

  26. ECE 301 - Digital Electronics Example: Given two functions, F1 and F2, of the same input variables x1.. x4, design the minimum-cost implementation.

  27. ECE 301 - Digital Electronics 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 F2 = X1'.X3 + X1.X3' + X2.X3.X4 Multiple-output Logic Circuit

  28. ECE 301 - Digital Electronics 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 Multiple-output Logic Circuit

  29. ECE 301 - Digital Electronics Example: Given two functions, F3 and F4, of the same input variables x1.. x4, design the minimum-cost implementation for the combined circuit. Note: the minimum-cost implementation for the combined circuit may not be the same as the minimum-cost implementations for the individual circuits.

  30. ECE 301 - Digital Electronics Multiple-output Logic Circuit 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 F4 = 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

  31. ECE 301 - Digital Electronics Multiple-output Logic Circuit 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' F4 = 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

  32. ECE 301 - Digital Electronics 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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