Introduction to Digital Logic Missouri S&T University CPE 2210 Exam 1 Logistics

Transcription

1 Introduction to Digital Logic Missouri S&T University CPE 2210 Exam 1 Logistics Egemen K. Çetinkaya Egemen K. Çetinkaya Department of Electrical & Computer Engineering Missouri University of Science and Technology cetinkayae@mst.edu 26 September 2016 rev Egemen K. Çetinkaya

2 Exam1 Logistics Overview Exam will be held on 28 September 2016 It will be in room ECE102 You are responsible from all material covered chapter readings from book lecture notes in-class discussions Cheating is prohibited! read course policies as a reminder Closed notes, books, no calculator Bring pencil and eraser 2

3 Exam1 Logistics Style Exam duration will be 50 minutes Exam will include different types of questions short answer long answer 3

4 Applications and History Binary logic is the basis for digital systems Early history goes to 1850s not much done till 1938 significant progress after World War II with invention of transistor last decade is head-spinning There are many application areas of digital systems very pervasive in our lives Analog signals are continuous signals Digital signals are discrete signals 4

5 Signals can be: analog: continuous digital: discrete Important terminology: bit, byte, nibble, LSB, MSB Number Systems Important number systems: decimal, binary, hex, octal Conversions will be needed throughout your careers: know by heart 5

6 Electric Circuits There are two types of digital circuits combinatorial circuits: no memory sequential circuits: memory Ohm s law: V=IR Switches are basic components of digital circuits Switches have two states: on and off Transistors are basic electric circuit component CMOS have NMOS and PMOS transistors together NMOS transistors conduct when gate is on PMOS transistors conduct when gate is off 6

7 Basic Logic Gates Logic gates building blocks of complex logic circuits Gate functions can be represented via: symbols truth tables equations timing diagrams transistor circuits Important three basic gates are: AND OR NOT 7

8 Boolean Algebra Understand the important Boolean algebra properties commutativity distributivity associativity identity complementery null elements idempotent law involution law DeMorgan s law absorption law 8

9 Boolean Representations Three Boolean representations: circuits equations truth tables Important terminology variables/literals product term/sum term/sum-of-products/product-of-sums normal term/minterm/maxterm canonical sum (sum-of-minterms) canonical product (product-of-maxterms) 9

10 Combinatorial Logic Circuit Design and Analysis Combinatorial logic circuit analysis truth table might be hard to construct for many inputs equations can be simplified via Boolean algebra circuits Combinatorial logic circuit design/synthesis capture behavior create equations simplify implement as a gate-based circuit 10

11 Logic Gates: NAND, NOR, XOR, XNOR Basic gates are: AND OR NOT More gates: NAND NOR XOR XNOR Universal gates: NAND & NOR 11

12 Real gates have delay Wires also have delay Practical Considerations Designer must consider critical path delay Attention to active-lows are required Simulations help analyze digital logic 12

13 Karnaugh Maps Karnaugh maps used to simplify truth tables Group together adjacent cells containing ones 1s grouping is done for a group of: 2 0, 2 1, 2 2 1s Every one must be in at least one group Each group should be as large as possible Fewest number of groups possible Overlapping of 1s is allowed Zeros are not allowed Diagonal groupings are not allowed For DC conditions; assign a 0 or a 1 and then simplify 13

14 Questions? 14