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

2. Remember Network • 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 . . . Outputs . . . Inputs Combinational Logic

3. 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 Combinational Logic

4. Basic Combinational Circuits • Adders • Multipliers • Multiplexers • Decoders • Encoders • Comparators • Subtractors Combinational Logic

5. 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 Combinational Logic

6. Example • Conversion from BCD to excess-5 Combinational Logic

7. Example (Cont.) Combinational Logic

8. Example (Cont.) Combinational Logic

9. Example (Cont.) Combinational Logic

10. 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 Combinational Logic

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

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

15. Question • How can you get 32-bit implementation? Combinational Logic

16. 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 • First take 1’s complement and add 1 Combinational Logic

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

18. Binary Multiplier From course book Combinational Logic

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

20. From course book Combinational Logic

21. Decoder • n by 2^n decoder • Converts information from n input lines into 2^n output lines • 2x4 Decoder • 3x8 Decoder Combinational Logic

22. 2x4 Decoder Combinational Logic

23. Internal Structure of 2x4 Decoder Combinational Logic

24. Another View Combinational Logic

25. From course book Combinational Logic

26. Example Combinational Logic

27. 4x16 Decoder From course book Combinational Logic

28. Full Adder with Decoder Combinational Logic

29. 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 Combinational Logic

30. 2x1 Multiplexer Combinational Logic

31. 4x1 Multiplexer Combinational Logic

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

33. Example Combinational Logic

34. Three-State Buffer Combinational Logic

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

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

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

38. Study Problem • Course Book Chapter – 4 Problems • 4 – 34 Combinational Logic

39. 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 Combinational Logic

40. Questions Combinational Logic