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DIGITAL LOGIC DESIGN

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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

  12. Full-Adder Combinational Logic

  13. Full-Adder HOW????? 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