Final Video PPT V_05 Final UNIT 3 part 2_DL and COA Programming.pptx
- 1. 1 DIGITAL LOGIC AND BASICS OF COMPUTER ORGANIZATION BCA DIGITAL LOGIC AND BASICS OF COMPUTER ORGANIZATION
- 2. 2 Unit 3: combinational circuits 1.0 Learning Outcome 1.1 Introduction 1.2 Multiplexer 1.3 Demultiplexer 1.4 Encoder 1.5 Decoder 1.6 Compartor DIGITAL LOGIC AND BASICS OF COMPUTER ORGANIZATION
- 3. 3 Unit 3: combinational circuits 1.7 Summary 1.8 Glossary 1.9 Self-Assessment Questions 1.10 Exam Oriented Questions 1.11 Suggested Readings DIGITAL LOGIC AND BASICS OF COMPUTER ORGANIZATION
- 4. 1.0 Learning Outcome After studying this unit, students will be able to: •Understand the working and internal logic of MUX, DEMUX, encoders, decoders, and comparators. •Design and implement data selection and distribution using multiplexers and demultiplexers. •Apply encoders and decoders for data compression and expansion in digital systems. DIGITAL LOGIC AND BASICS OF COMPUTER ORGANIZATION 4
- 5. 1.0 Learning Outcome (contd.) After studying this unit, students will be able to: •Perform binary comparisons using comparator logic for control and decision-making. •Use truth tables and logic expressions to analyze and construct combinational circuits. DIGITAL LOGIC AND BASICS OF COMPUTER ORGANIZATION 5
- 6. 1.1 Introduction •Modern digital systems involve constant decision-making, data routing, and conversion between formats. To handle these operations, we rely on efficient combinational circuits such as multiplexers, demultiplexers, encoders, decoders, and comparators. •A multiplexer (MUX) selects one input from many and routes it to a single output. DIGITAL LOGIC AND BASICS OF COMPUTER ORGANIZATION 6
- 7. 1.1 Introduction • A demultiplexer (DEMUX) performs the reverse, sending one input to a selected output line. • An encoder compresses data by converting multiple inputs into a binary code. • A decoder expands a binary input into multiple outputs — often used in memory addressing or displays. • A comparator compares two binary numbers and determines if one is greater, equal to, or less than the other. DIGITAL LOGIC AND BASICS OF COMPUTER ORGANIZATION 7
- 8. DIGITAL LOGIC AND BASICS OF COMPUTER ORGANIZATION 8 A multiplexer has N control inputs 2N data inputs 1 output A multiplexer routes (or connects) the selected data input to the output. The value of the control inputs determines the data input that is selected. 1.2 Multiplexers
- 9. 9 1.2 Multiplexers Z = A′.I0 + A.I1 Data inputs Control input DIGITAL LOGIC AND BASICS OF COMPUTER ORGANIZATION
- 10. 10 1.2 Multiplexers Z = A′.B'.I0 + A'.B.I1 + A.B'.I2 + A.B.I3 A B F 0 0 I0 0 1 I1 1 0 I2 1 1 I3 MSB LSB DIGITAL LOGIC AND BASICS OF COMPUTER ORGANIZATION
- 11. 11 1.3 Demultiplexers A demultiplexer has N control inputs 1 data input 2N outputs A demultiplexer routes (or connects) the data input to the selected output. The value of the control inputs determines the output that is selected. A demultiplexer performs the opposite function of a multiplexer. DIGITAL LOGIC AND BASICS OF COMPUTER ORGANIZATION
- 12. 12 Demultiplexers A B W X Y Z 0 0 I 0 0 0 0 1 0 I 0 0 1 0 0 0 I 0 1 1 0 0 0 I W = A'.B'.I X = A.B'.I Y = A'.B.I Z = A.B.I Out0 In S1 S0 I W X Y Z A B Out1 Out2 Out3 DIGITAL LOGIC AND BASICS OF COMPUTER ORGANIZATION
- 13. 13 1.4 Encoders An encoder has 2N inputs N outputs An encoder outputs the binary value of the selected (or active) input. An encoder performs the inverse operation of a decoder. Issues What if more than one input is active? What if no inputs are active? DIGITAL LOGIC AND BASICS OF COMPUTER ORGANIZATION
- 14. 14 1.4 Encoders A B C D Y Z 0 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 1 0 1 0 0 0 1 1 D Z Y I0 I1 C B I2 I3 A Out0 Out1 DIGITAL LOGIC AND BASICS OF COMPUTER ORGANIZATION
- 15. 15 Priority Encoders If more than one input is active, the higher-order input has priority over the lower-order input. The higher value is encoded on the output A valid indicator, d, is included to indicate whether or not the output is valid. Output is invalid when no inputs are active d = 0 Output is valid when at least one input is active d = 1 DIGITAL LOGIC AND BASICS OF COMPUTER ORGANIZATION
- 16. 16 1.5 Decoders A decoder has N inputs 2N outputs A decoder selects one of 2N outputs by decoding the binary value on the N inputs. The decoder generates all of the minterms of the N input variables. Exactly one output will be active for each combination of the inputs. DIGITAL LOGIC AND BASICS OF COMPUTER ORGANIZATION
- 17. 17 1.5 Decoders A B W X Y Z 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 1 1 0 0 0 1 Active-high outputs B W X Y Z I0 I1 A Out0 Out1 Out2 Out3 W = A'.B' X = A.B' Y = A'.B Z = A.B msb DIGITAL LOGIC AND BASICS OF COMPUTER ORGANIZATION
- 18. DIGITAL LOGIC AND BASICS OF COMPUTER ORGANIZATION 18 • A comparator is a combinational circuit • Compares two binary numbers (A and B) • Produces outputs to indicate: a) A > B b) A = B c) A < B 1.6 Comparator
- 19. DIGITAL LOGIC AND BASICS OF COMPUTER ORGANIZATION 19 • 1-bit Comparator • Multi-bit Comparator (e.g., 2-bit, 4-bit, 8-bit) • Cascadable Comparator (used to build larger comparators) 1.6 Comparator
- 20. DIGITAL LOGIC AND BASICS OF COMPUTER ORGANIZATION 20 Inputs: A, B Outputs: •A > B = A · B ̅ •A = B = · + A · B A ̅ B ̅ •A < B = · B A ̅ A B A > B A = B A < B 0 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 0 1 0
- 21. 1.7 Summary(Contd.) • Multiplexer (MUX): A data selector that forwards one of many inputs to a single output line based on select inputs. • Demultiplexer (DEMUX): A data distributor that sends a single input to one of many outputs using control lines. • Encoder: Converts active input lines into a binary code. Priority encoders resolve conflicts when multiple inputs are active. DIGITAL LOGIC AND BASICS OF COMPUTER ORGANIZATION 21
- 22. 1.7 Summary(Contd.) • Decoder: Translates binary inputs into uniquely activated outputs; often used in display drivers and memory addressing. • Comparator: Compares binary numbers and generates output signals for greater than, equal to, or less than conditions. DIGITAL LOGIC AND BASICS OF COMPUTER ORGANIZATION 22
- 23. 1.8 Glossary(Contd.) DIGITAL LOGIC AND BASICS OF COMPUTER ORGANIZATION 23 Term Definition MUX Multiplexer – selects one of many input lines and forwards it to the output DEMUX Demultiplexer – routes one input to one of many output lines Encoder Converts multiple input lines into a smaller number of binary outputs Decoder Converts binary inputs into uniquely active outputs
- 24. 1.8 Glossary(Contd.) DIGITAL LOGIC AND BASICS OF COMPUTER ORGANIZATION 24 Comparator A circuit that compares two binary numbers and outputs their relationship Select Lines Control inputs that determine the active input/output in MUX/DEMUX Priority Encoder An encoder that assigns output based on the highest-priority active input Cascading Connecting smaller circuits (like comparators) together for larger operations
- 25. 1.9 Self-Assessment(Cont.) •What is a multiplexer? How does a 4-to-1 multiplexer work? •Differentiate between a multiplexer and a demultiplexer with examples. •Write the truth table for a 3-to-8 decoder. How many outputs does it have? •What is the main function of an encoder? Why is a priority encoder used? DIGITAL LOGIC AND BASICS OF COMPUTER ORGANIZATION 25
- 26. 1.10 Exam-Oriented Questions •Short Answer: •What is the function of a multiplexer? Give a real- world example. •Write the truth table for a 2-to-4 decoder. •Differentiate between encoder and decoder DIGITAL LOGIC AND BASICS OF COMPUTER ORGANIZATION 26
- 27. 1.10 Exam-Oriented Questions •Explain the working of a 1-to-4 demultiplexer with a logic diagram. •Describe the operation of a priority encoder with a suitable truth table and circuit. •What is a 3-to-8 decoder? Explain how it is used for memory address decoding. DIGITAL LOGIC AND BASICS OF COMPUTER ORGANIZATION 27
- 28. 1.11 Suggested Readings •"Digital Design" by M. Morris Mano – Pearson Education •"Digital Fundamentals" by Thomas L. Floyd – Pearson •"Modern Digital Electronics" by R. P. Jain – McGraw Hill DIGITAL LOGIC AND BASICS OF COMPUTER 28
- 29. 29 DIGITAL LOGIC AND BASICS OF COMPUTER ORGANIZATION