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Logic Circuit Design Concepts in Digital Electronics

Understand the process of designing combinational logic circuits for digital electronics, including specifications, implementation, and verification steps. Learn about tradeoffs and hierarchical design to solve complex design problems effectively.

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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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