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

2. ECE 301 - Digital Electronics2 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 Electronics3 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 Electronics4 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 Electronics5 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 Electronics6 Example: Design a combinational logic circuit that compares two 2-bit numbers, A (a 1 a 0 ) and B (b 1 b 0 ), and outputs a 1 when A > B. Logic Circuit Design

7. ECE 301 - Digital Electronics7 To implement the design, follow the 5 steps specified in the Design Process.

8. ECE 301 - Digital Electronics8 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 Electronics9 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 Electronics10 2. Determine Inputs and Outputs Input: Binary Coded Decimal value Logic Circuit Design

11. ECE 301 - Digital Electronics11 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 Electronics12 Binary Coded Decimal Decimal DigitBCD Code 00000 10001 20010 30011 40100 50101 60110 70111 81000 91001

13. ECE 301 - Digital Electronics13 2. Determine Inputs and Outputs Output: Excess-3 Code value Logic Circuit Design

14. ECE 301 - Digital Electronics14 Excess-3 Code Decimal DigitExcess-3 Code 00011 10100 20101 30110 40111 51000 61001 71010 81011 91100

15. ECE 301 - Digital Electronics15 3. Derive Truth Table Logic Circuit Design

16. ECE 301 - Digital Electronics16 Code Conversion

17. ECE 301 - Digital Electronics17 4. Determine simplified Boolean expression(s) Logic Circuit Design

18. ECE 301 - Digital Electronics18 Code Conversion

19. ECE 301 - Digital Electronics19 Code Conversion

20. ECE 301 - Digital Electronics20 Code Conversion

21. ECE 301 - Digital Electronics21 Code Conversion

22. ECE 301 - Digital Electronics22 5. Implement Solution Logic Circuit Design

23. ECE 301 - Digital Electronics23 Code Converter

24. ECE 301 - Digital Electronics24 6. Verify Solution (Analyze, Simulate, or Test the Logic Circuit) Logic Circuit Design

25. ECE 301 - Digital Electronics25 Multiple-Output Logic Circuits

26. ECE 301 - Digital Electronics26 Example: Given two functions, F 1 and F 2, of the same input variables x 1.. x 4, design the minimum-cost implementation.

27. ECE 301 - Digital Electronics27 x 1 x 2 x 3 x 4 00011110 11 11 11 11 00 01 11 10 (a) Function 1 f 1 F1 = X1'.X3 + X1.X3' + X2.X3'.X4 x 1 x 2 x 3 x 4 00011110 11 11 111 11 00 01 11 10 (b) Function f 2 F2 = X1'.X3 + X1.X3' + X2.X3.X4 Multiple-output Logic Circuit

28. ECE 301 - Digital Electronics28 f 1 f 2 x 2 x 3 x 4 x 1 x 3 x 1 x 3 x 2 x 3 x 4 (c) Combined circuit for f 1 f 2 and Multiple-output Logic Circuit

29. ECE 301 - Digital Electronics29 Example: Given two functions, F 3 and F 4, of the same input variables x 1.. x 4, 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 Electronics30 x 1 x 2 x 3 x 4 00011110 1 11 1 00 01 11 10 (a) Optimal realization of(b) Optimal realization of 1 f 3 f 4 1 1 x 1 x 2 x 3 x 4 00011110 11 1 1 00 01 11 10 1 11 F3 = X1'.X4 + X2.X4 + X1'.X2.X3F4 = 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 Multiple-output Logic Circuit

31. ECE 301 - Digital Electronics31 (c) Optimal realization of f 3 x 1 x 2 x 3 x 4 00011110 1 11 1 00 01 11 10 11 1 x 1 x 2 x 3 x 4 00011110 11 1 1 00 01 11 10 1 11 andtogether f 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 Total Gates and Inputs required: 6 Logic Gates 17 Inputs shared logic gates Multiple-output Logic Circuit

32. ECE 301 - Digital Electronics32 f 3 f 4 x 1 x 4 x 3 x 4 x 1 x 1 x 2 x 2 x 4 x 4 (d) Combined circuit for f 3 f 4 and x 2 Multiple-output Logic Circuit