1. Combinational Logic1 DIGITAL LOGIC DESIGN by Dr. Fenghui Yao Tennessee State University Department of Computer Science Nashville, TN

2. Combinational Logic2 Remember  Combinational  The outputs depend only on the current input values  It uses only logic gates  Sequential  The outputs depend on the current and past input values  It uses logic gates and storage elements Network............ Inputs Outputs

3. Combinational Logic3 Notes  If there are n input variables, there are 2^n input combinations  For each input combination, there is one output value  Truth tables are used to list all possible combinations of inputs and corresponding output values

4. Combinational Logic4 Basic Combinational Circuits  Adders  Multipliers  Multiplexers  Decoders  Encoders  Comparators  Subtractors

5. Combinational Logic5 Design  Determine the inputs and outputs  Assign a symbol for each  Derive the truth table  Get the simplified boolean expression for each output  Draw the network diagram

6. Combinational Logic6 Example  Conversion from BCD to excess-5

7. Combinational Logic7 Example (Cont.)

8. Combinational Logic8 Example (Cont.)

9. Combinational Logic9 Example (Cont.)

10. Combinational Logic10 Adders  Essential part of every CPU  Half adder (Ignore the carry-in bit)  It performs the addition of two bits  Full adder  It performs the addition of three bits

11. Combinational Logic11 Half-Adder  You can use K-Map to simplify  It is also obvious from the truth table

12. Combinational Logic12 Full-Adder

13. Combinational Logic13 Full-Adder HOW?????

14. Combinational Logic14 4-bit Adder Implementation From course book

15. Combinational Logic15 Question  How can you get 32-bit implementation?

16. Combinational Logic16 Binary Subtractor  Remember  You need to take 2’s complement to represent negative numbers  A-B Take 2’s complement of B and add it to A Take 2’s complement of B and add it to A  First take 1’s complement and add 1

17. Combinational Logic17 4-Bit Adder and Subtractor From course book

18. Combinational Logic18 Binary Multiplier From course book

19. Combinational Logic19 Comparators  Compare two input words  Returns 1 if A=B, 0 otherwise

20. Combinational Logic20 From course book

21. Combinational Logic21 Decoder  n by 2^n decoder  Converts information from n input lines into 2^n output lines  2x4 Decoder  3x8 Decoder

22. Combinational Logic22 2x4 Decoder

23. Combinational Logic23 Internal Structure of 2x4 Decoder

24. Combinational Logic24 Another View

25. Combinational Logic25 From course book

26. Combinational Logic26 Example

27. Combinational Logic27 4x16 Decoder From course book

28. Combinational Logic28 Full Adder with Decoder

29. Combinational Logic29 Multiplexers  You can select information from one of many input lines and assign it to one output line  You have input lines, control lines, and one output line  It is called MUX

30. Combinational Logic30 2x1 Multiplexer

31. Combinational Logic31 4x1 Multiplexer

32. Combinational Logic32 Boolean Function Implementation How do you implement it with 8x1 MUX?

33. Combinational Logic33 Example

34. Combinational Logic34 Three-State Buffer

35. Combinational Logic35 2x1 MUX with Three-State Buffer

36. Combinational Logic36 Shifters  8-input, 8-output shifter  C=1 => right shift, C=0 => left shift

37. Combinational Logic37 Study Problem  Course Book Chapter – 4 Problems  4 – 31 Construct a 16x1 multiplexer with two 8x1 and one 2x1 multiplexer. Use block diagrams Construct a 16x1 multiplexer with two 8x1 and one 2x1 multiplexer. Use block diagrams

38. Combinational Logic38 Study Problem  Course Book Chapter – 4 Problems  4 – 34

39. Combinational Logic39 Study Problems  Course Book Chapter – 4 Problems  4 – 1  4 – 4  4 – 6  4 – 11  4 – 20  4 – 21  4 – 25  4 – 32  4 – 33  4 – 35

40. Combinational Logic40 Questions