EE100Su08 Lecture 16 August 1st 2008 OUTLINE Project next week Pick up kits in your first lab section work on the project in your first lab section at home etc and wrap up in the second lab section USE MULTISIM TO SIMULATE PROJECT REFER TO MULTISIM FILE ONLINE HW 3s 6s Pick up from lab regrades talk to Bart Introduction to Boolean Algebra and Digital Circuits Diode Logic Transistor introduction MOSFETs Transistor logic circuits Reading Reader Chapter 2 Chapter 4 and 5 for transistors just concentrate on logic applications EE100 Summer 2008 Slide 1 Bharathwaj Muthuswamy EE100 Summer 2008 Slide 2 Bharathwaj Muthuswamy Analog vs Digital Signals Most but not all observables are analog think of analog vs digital watches but the most convenient way to represent transmit information electronically is to use digital signals think of a computer EE100 Summer 2008 Slide 3 Bharathwaj Muthuswamy Digital Signal Representations Binary numbers can be used to represent any quantity Counting EE100 Summer 2008 Slide 4 Bharathwaj Muthuswamy Digital Signal Representations Binary numbers can be used to represent any quantity Counting EE100 Summer 2008 Slide 5 Bharathwaj Muthuswamy Decimal Numbers Base 10 Digits 0 1 2 3 4 5 6 7 8 9 Example 3271 3x103 2x102 7x101 1x100 This is a four digit number The left hand most number 3 in this example is often referred as the most significant number and the right most the least significant number 1 in this example EE100 Summer 2008 Slide 6 Bharathwaj Muthuswamy Numbers positional notation Number Base B B symbols per digit Base 10 Decimal Base 2 Binary 0 1 2 3 4 5 6 7 8 9 0 1 Number representation d31d30 d1d0 is a 32 digit number value d31 B31 d30 B30 d1 B1 d0 B0 Binary 0 1 In binary digits called bits 11010 1 24 1 23 0 22 1 21 0 20 16 8 2 26 Here 5 digit binary turns into a 2 digit decimal EE100 Summer 2008 Slide 7 Bharathwaj Muthuswamy Hexadecimal Numbers Base 16 Hexadecimal 0 1 2 3 4 5 6 7 8 9 A B C D E F Normal digits 6 more from the alphabet Conversion Binary Hex 1 hex digit represents 16 decimal values 4 binary digits represent 16 decimal values 1 hex digit replaces 4 binary digits EE100 Summer 2008 Slide 8 Bharathwaj Muthuswamy Decimal Binary Conversion Decimal to Binary Repeated Division By 2 Consider the number 2671 Subtraction if you know your 2N values by heart Binary to Decimal conversion 1100012 1x25 1x24 0x23 0x22 0x21 1x20 3210 1610 110 4910 4x101 9x100 EE100 Summer 2008 Slide 9 Bharathwaj Muthuswamy Example Possible digital representation for the sine wave signal EE100 Summer 2008 Analog representation Amplitude in V 1 2 3 4 5 Digital representation Binary number 000001 000010 000011 000100 000101 8 001000 16 010000 32 100000 50 110010 63 111111 Slide 10 Bharathwaj Muthuswamy Binary Representation N bit can represent 2N values typically from 0 to 2N 1 3 bit word can represent 8 values e g 0 1 2 3 4 5 6 7 Conversion Integer to binary Fraction to binary 13 510 1101 12 and 0 39210 0 0110012 Octal and hexadecimal EE100 Summer 2008 Slide 11 Bharathwaj Muthuswamy Logic Gates Logic gates Combine several logic variable inputs to produce a logic variable output Memory Memoryless output at a given instant depends the input values of that instant Memory output depends on previous and present input values EE100 Summer 2008 Slide 12 Bharathwaj Muthuswamy Boolean algebras Algebraic structures capture the essence of the logical operations AND OR and NOT corresponding set for theoretic operations intersection union and complement named after George Boole an English mathematician at University College Cork who first defined them as part of a system of logic in the mid 19th century Boolean algebra was an attempt to use algebraic techniques to deal with expressions in the propositional calculus Today Boolean algebras find many applications in electronic design They were first applied to switching by Claude Shannon in the 20th century EE100 Summer 2008 Slide 13 Bharathwaj Muthuswamy Boolean algebras The operators of Boolean algebra may be represented in various ways Often they are simply written as AND OR and NOT In describing circuits NAND NOT AND NOR NOT OR and XOR eXclusive OR may also be used Mathematicians often use for OR and for AND since in some ways those operations are analogous to addition and multiplication in other algebraic structures and represent NOT by a line drawn above the expression being negated EE100 Summer 2008 Slide 14 Bharathwaj Muthuswamy Logic Functions Symbols Notation NAME NOT OR AND SYMBOL A A B A B EE100 Summer 2008 F F F Slide 15 NOTATION TRUTH TABLE F A A F 0 1 1 0 F A B A B 0 0 0 1 1 0 1 1 F 0 1 1 1 F A B A B 0 0 0 1 1 0 1 1 F 0 0 0 1 Bharathwaj Muthuswamy Logic Functions Symbols Notation 2 NOR NAND XOR exclusive OR A B A B A B EE100 Summer 2008 F F F Slide 16 F A B A B 0 0 0 1 1 0 1 1 F 1 0 0 0 F A B A B 0 0 0 1 1 0 1 1 F 1 1 1 0 F A B A B 0 0 0 1 1 0 1 1 F 0 1 1 0 Bharathwaj Muthuswamy EE100 Summer 2008 Slide 17 Bharathwaj Muthuswamy EE100 Summer 2008 Slide 18 Bharathwaj Muthuswamy Boolean Algebra NOT operation inverter AND operation AgA 0 A A 1 AgA A Ag1 A Ag0 0 AgB B gA OR operation AgB gC Ag B gC A A A A 1 1 A 0 A A B B A A B C A B C EE100 Summer 2008 Slide 19 Bharathwaj Muthuswamy Boolean Algebra Distributive Property Ag B C AgB AgC A B gC A B g A C De Morgan s laws A B AgB AgB A B An excellent web site to visit http en wikipedia org wiki Boolean algebra EE100 Summer 2008 Slide 20 Bharathwaj Muthuswamy Circuit Realization Three input adder with carry EE100 Summer 2008 Slide 21 Bharathwaj Muthuswamy Diode Logic AND Gate Diodes can be used to perform logic functions AND gate output voltage is high only if both A and B are high Vcc Inputs A and B vary between 0 Volts low and Vcc high Between what voltage levels does C vary RAND A C B EE100 Summer 2008 Slide 22 Bharathwaj Muthuswamy Diode Logic Incompatibility and Decay Diode Only Gates are Basically Incompatible AND gate OR gate output voltage is high only if both A and B are high output voltage is high if either or both A and B are high Vcc A RAND A B COR CAND B ROR CAND High want RAND ROR CAND Low want RAND ROR Signal Decays with each stage Not regenerative EE100 Summer 2008 Slide 23 Bharathwaj Muthuswamy MOSFETs Detailed outline OUTLINE The MOSFET as a controlled resistor MOSFET ID vs VGS characteristic NMOS and PMOS I V characteristics Simple …
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