Digital Logic & Design
- 1. Digital Logic & Design Lecture 01 Rubya Afrin Lecturer Northern University of Business and Technology
- 2. Course Outline CSE 1205: Digital Logic Design C. Hrs. 3.00 Digital logic, Boolean algebra, De Morgan’s Theorem, Boolean function, Canonical forms, Minimization of Boolean functions, Logic gates and their truth tables, Canonical forms, Minimization technique, Arithmetic and data handling logic circuits. Decoders, Encoders, Multiplexer, De-multiplexer. Combinational Circuit Design, Electronic circuits for flip-flop, counters, registers and memory devices. PLA design, Synchronous and asynchronous logic design, state diagram, Mealy and Moore machine, state minimization and assignments, pulse mode design, Fundamental mode design. Recommended books: 1. Digital Logic & Computer Design : Morris Mano 2. Digital Systems: Principles and : Ronald J. Tocci, Neal S. Widmar, 3. Applications Gregory L. Moss
- 3. Grading Attendance 5 Class test, Assignment, Presentation 25 Mid Term 30 Final Exam 40 Total 100
- 4. Analogue Quantities Continuous Quantity Intensity of Light Temperature Velocity
- 5. Digital Values Discrete set of values
- 6. Continuous Signal 0 5 10 15 20 25 30 35 40 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 time temperature0 C
- 7. Digital Representation 1 2 4 7 18 34 25 23 35 37 29 42 41 25 22 0 5 10 15 20 25 30 35 40 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 samples temperature0 C
- 8. Digital Systems Two Voltage Levels Two States On/Off Black/White Hot/Cold Stationary/Moving
- 9. Binary Number System Binary Numbers Representing Multiple Values Combination of 0v & 5v
- 10. Logic Gates Building Blocks AND, OR and NOT Gates NAND, NOR, XOR and XNOR Gates Integrated Circuits (ICs)
- 11. Logic Gate Symbol and ICs 1 2 3 4 5 6 GND Vcc 13 12 11 10 9 8 7400
- 12. Combinational Circuits Combination of Logic Gates Adder Combinational Circuit
- 14. Functional Devices Functional Devices Adders Comparators Encoders/Decoders Multiplexers/Demultiplexers
- 15. Sequential Circuits Memory Element Current & Previous State Flip-Flops Counters & Registers
- 16. Block Diagram of a Sequential Circuit
- 17. Programmable Logic Devices (PLDs) Configurable Hardware Combinational Circuits Sequential Circuits Low chip count Lower Cost Short development time
- 18. Memory Storage RAM (Random Access Memory) Read-Write Volatile ROM (Read-Only Memory) Read-Only Non-Volatile
- 19. Binary Number System Two unique numbers 0 and 1 Base – 2 A binary digit is a bit Combination of bits to represent larger values
- 20. Binary Number System Decimal Number Binary Number Decimal Number Binary Number 0 0 10 1010 1 1 11 1011 2 10 12 1100 3 11 13 1101 4 100 14 1110 5 101 15 1111 6 110 16 10000 7 111 17 10001 8 1000 18 10010 9 1001 19 10011
- 21. Combination of Binary Bits Combination of Bits 100112 = 1910 = (1 x 24 ) + (0 x 23 ) + (0 x 22 ) + (1 x 21 ) + (1 x 20 ) = (1 x 16) + (0 x 8) + (0 x 4) + (1 x 2) + (1 x 1) = 16 + 0 + 0 + 2 + 1 = 19
- 22. Fractions in Binary Fractions in Binary 1011.1012 = 11.625 = (1 x 23 ) + (0 x 22 ) + (1 x 21 ) + (1 x 20 )+ (1 x 2-1 ) + (0 x 2-2 ) + (1 x 2-3 ) = (1 x 8) + (0 x 4) + (1 x 2) + (1 x 1)+ (1 x 1/2) + (0 x 1/4) + (1 x 1/8) = 8 + 0 + 2 + 1 + 0.5 + 0 + 0.125 = 11.625 Floating Point Notations
- 23. Decimal-Binary Conversion Binary to Decimal Conversion Sum-of-Weights Adding weights of non-zero terms Decimal to Binary Conversion Sum-of-Weights (in reverse) Repeated Division by 2
- 24. Number Weight Result after subtraction Binary 392 256 392-256=136 1 136 128 136-128=8 1 8 54 0 8 32 0 8 16 0 8 8 8-8=0 1 0 4 0 0 2 0 0 1 0 Decimal to binary conversion using Sum of weight
- 25. Decimal-Binary Conversion Binary to Decimal Conversion Sum-of-Weights Adding weights of non-zero terms 2 4 3 2 1 0 10011 (1 2 ) (0 2 ) (0 2 ) (1 2 ) (1 2 ) × + × + × + × + × Terms 16,0,0.2 and 1 19
- 26. 2’s Complement form 1’s complement form 2’s complement form Binary number 01101 (13) 1’s complement 10010 + 1 2’s complement 10011 (-13)
- 27. Addition and Subtraction with 2’s Complement 0101 +5 0101 +5 0010 +2 1110 -2 0111 +7 10011 +3 1011 -5 1011 -5 1110 -2 0010 +2 11001 -7 1101 -3
- 28. BCD (Binary Coded Decimal) Code Decimal BCD Decimal BCD 0 0000 5 0101 1 0001 6 0110 2 0010 7 0111 3 0011 8 1000 4 0100 9 1001
- 29. BCD Addition Multi-digit BCD numbers can be added together 23 0010 0011 45 0100 0101 68 0110 1000 23 0010 0011 48 0100 1000 71 0110 1011 1011 is illegal BCD number
- 30. BCD Addition Add a 0110 (6) to an invalid BCD number Carry added to the most significant BCD digit 23 0010 0011 48 0100 1000 71 0110 1011 0110 0111 0001
- 31. Logic Gates Basic Building Blocks Logic Gate Symbol Unique function Truth or Function Table Function Expression Timing Diagram
- 32. AND Gate 1 output 2 inputs 3 inputs 4 inputs Multiple inputs
- 33. AND Gate function Input Output A B F 0 0 0 0 1 0 1 0 0 1 1 1 Logical Multiplication function BAF •= NCBAF ••••= ....
- 34. AND Gate Timing Diagram
- 35. OR Gate 1 output 2 inputs 3 inputs 4 inputs Multiple inputs
- 36. OR Gate function Input Output A B F 0 0 0 0 1 1 1 0 1 1 1 1 Boolean Add function BAF += NCBAF ++++= ..
- 37. OR Gate Timing Diagram
- 38. NOT Gate 1 input 1 output
- 39. NOT Gate function Input Output A F 0 1 1 0 Invert function AF =
- 40. NOT Gate Timing Diagram
- 41. AND Gate Applications Enable/Disable Device Counter counts when it receives pulses
- 42. NOT Gate Applications 1’s Complement
- 44. NAND Gate 1 output 2 inputs 3 inputs 4 inputs Multiple inputs
- 45. NAND Gate function Input Output A B F 0 0 1 0 1 1 1 0 1 1 1 0 NOT-AND function BAF •= NCBAF ••••= ....
- 46. NAND Gate Timing Diagram t0 t4 t5 t6 t1 t2 t3 A B F
- 47. NAND Universal Gate Input Output A B F 0 0 1 0 1 1 1 0 1 1 1 0
- 48. NAND Universal Gate Input Output Output A B F1 F 0 0 1 0 0 1 1 0 1 0 1 0 1 1 0 1
- 49. NAND Universal Gate Input Output A B F 0 0 0 0 1 1 1 0 1 1 1 1
- 50. NOR Gate 1 output 2 inputs 3 inputs 4 inputs Multiple inputs
- 51. NOR Gate function Input Output A B F 0 0 1 0 1 0 1 0 0 1 1 0 NOT-OR function BAF += NCBAF ++++= ....
- 52. NOR Gate Timing Diagram
- 53. Home work: NOR Universal Gate
- 54. Questions???
- 55. Thank You…