EE100Su08 Lecture #16 (August 1st 2008)Slide 2Analog vs. Digital SignalsDigital Signal RepresentationsSlide 5Decimal Numbers: Base 10Numbers: positional notationHexadecimal Numbers: Base 16Decimal-Binary ConversionExampleBinary RepresentationLogic GatesBoolean algebrasSlide 14Logic Functions, Symbols, & NotationLogic Functions, Symbols, & Notation 2Slide 17Slide 18Boolean AlgebraSlide 20Circuit Realization: Three input adder with carryDiode Logic: AND GateDiode Logic: Incompatibility and DecayMOSFETs: Detailed outlineMOSFETSlide 26MOSFET Operating RegionsInverter = NOT GateNMOS Resistor Pull-UpDisadvantages of NMOS Logic GatesThe CMOS Inverter: Intuitive PerspectiveFeatures of CMOS Digital CircuitsNMOS NAND GateNMOS NOR GateN-Channel MOSFET OperationP-Channel MOSFET OperationPull-Down and Pull-Up DevicesCMOS NAND GateCMOS NOR GateSlide 1EE100 Summer 2008 Bharathwaj MuthuswamyEE100Su08 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).Slide 2EE100 Summer 2008 Bharathwaj MuthuswamySlide 3EE100 Summer 2008 Bharathwaj Muthuswamy• Most (but not all) observables are analogthink of analog vs. digital watchesbut the most convenient way to represent & transmit information electronically is to use digital signalsthink of a computer!Analog vs. Digital SignalsSlide 4EE100 Summer 2008 Bharathwaj MuthuswamyDigital Signal RepresentationsBinary numbers can be used to represent any quantity. Counting:Slide 5EE100 Summer 2008 Bharathwaj MuthuswamyDigital Signal RepresentationsBinary numbers can be used to represent any quantity. Counting:Slide 6EE100 Summer 2008 Bharathwaj MuthuswamyDecimal Numbers: Base 10Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9Example: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).Slide 7EE100 Summer 2008 Bharathwaj MuthuswamyNumbers: positional notation•Number Base B B symbols per digit:–Base 10 (Decimal): 0, 1, 2, 3, 4, 5, 6, 7, 8, 9–Base 2 (Binary): 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 = 124 + 123 + 022 + 121 + 020 = 16 + 8 + 2= 26–Here 5 digit binary # turns into a 2 digit decimal #Slide 8EE100 Summer 2008 Bharathwaj MuthuswamyHexadecimal 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: BinaryHex–1 hex digit represents 16 decimal values–4 binary digits represent 16 decimal values1 hex digit replaces 4 binary digitsSlide 9EE100 Summer 2008 Bharathwaj MuthuswamyDecimal-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 conversion1100012 = 1x25 +1x24 +0x23 +0x22 + 0x21 + 1x20 = 3210 + 1610 + 110 = 4910 = 4x101 + 9x100Slide 10EE100 Summer 2008 Bharathwaj MuthuswamyPossible digital representation for the sine wave signal:Analog representation: Digital representation:Amplitude in VBinary number1 0000012 0000103 0000114 0001005 0001018 00100016 01000032 10000050 11001063 111111ExampleSlide 11EE100 Summer 2008 Bharathwaj MuthuswamyBinary 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 hexadecimalSlide 12EE100 Summer 2008 Bharathwaj MuthuswamyLogic 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.Slide 13EE100 Summer 2008 Bharathwaj MuthuswamyBoolean 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.Slide 14EE100 Summer 2008 Bharathwaj MuthuswamyBoolean 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.Slide 15EE100 Summer 2008 Bharathwaj MuthuswamyLogic Functions, Symbols, & Notation“NOT”F = ATRUTHNAME SYMBOL NOTATION TABLEFAA B F0 0 00 1 01 0 01 1 1“OR”F = A+BFABA F0 11 0A B F0 0 00 1 11 0 11 1 1“AND”F = A•BFABSlide 16EE100 Summer 2008 Bharathwaj MuthuswamyLogic Functions, Symbols, & Notation 2“NOR”F = A+BA B F0 0 00 1 11 0 11 1 0“NAND”F = A•BFABA B F0 0 10 1 11 0 11 1 0“XOR”(exclusive OR)F = A + BFABFABA B F0 0 10 1 01 0 01 1 0Slide 17EE100 Summer 2008 Bharathwaj MuthuswamySlide 18EE100 Summer 2008 Bharathwaj MuthuswamySlide 19EE100 Summer 2008 Bharathwaj MuthuswamyBoolean Algebra•NOT operation (inverter) •AND operation•OR operation01A AA A=+ =g10 0( ) ( )A A AA AAA B B AA B C A B C=====gggg gg g g g1 10( ) ( )A A AAA AA B B AA B C A B C+ =+ =+ =+ = ++ + = + +Slide 20EE100 Summer 2008 Bharathwaj MuthuswamyBoolean
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