2Transistor: Building Block of Computers Microprocessors contain millions of transistorsIntel Pentium II: 7 millionCompaq Alpha 21264: 15 millionIntel Pentium III: 28 millionIntel Pentium4: 55 MillionIntel Core 2 Duo: 291 MillionLogically, each transistor acts as a switchCombined to implement logic functionsAND, OR, NOTCombined to build higher-level structuresAdder, multiplexor, decoder, register, …Combined to build processorLC-3
3Transistors http://www.brew-wood.co.uk/computers/transistor.htm First transistor: Bell Labs in 1947; developed byJ. Bardeen, W. Shockley & W. BrattainA 2011 processor with 1.17 billion transistors positioned in 240 sq. millimeters
4Simple Switch Circuit Switch open: Switch closed: No current through circuitLight is offVout is +2.9VSwitch closed:Short circuit across switchCurrent flowsLight is onVout is 0VSwitch-based circuits can easily represent two states:on/off, open/closed, voltage/no voltage.
5N-type MOS Transistor MOS = Metal Oxide Semiconductor N-type Gate = 1 two types: N-type and P-typeN-typewhen Gate has positive voltage, short circuit between #1 and #2 (switch closed)when Gate has zero voltage, open circuit between #1 and #2 (switch open)Gate = 1DrainAnimationGate = 0SourceGNDTerminal #2 must beconnected to GND (0V).GND
6P-type MOS Transistor P-type is complementary to N-type Gate = 1 +2.9V when Gate has positive voltage, open circuit between #1 and #2 (switch open)when Gate has zero voltage, short circuit between #1 and #2 (switch closed)Gate = 1+2.9VGNDSourceGate = 0DrainTerminal #1 must beconnected to +2.9V.
7CMOS Circuit Complementary MOS Uses both N-type and P-type MOS transistorsP-typeAttached to + voltagePulls output voltage UP when input is zeroN-typeAttached to GNDPulls output voltage DOWN when input is oneFor all inputs, make sure that output is either connected to GND or to +, but not both!
8Inverter (NOT Gate) High Voltage Truth table Ground In Out 0 V 2.9 V 1
9Logical OperationsIn 1850, George Boole developed Boolean Algebra showing that all logical functions can be performed with just 3 operations (AND, OR & NOT). In 1937, Claude Shannon showed that Boolean Algebra could be applied to circuit design.
10NOR Gate (NOT OR) High Voltage Ground A B C 1 1GroundNote: Serial structure on top, parallel on bottom.
15More than 2 Inputs? AND/OR can take any number of inputs. AND = 1 if all inputs are 1.OR = 1 if any input is 1.Similar for NAND/NOR.An AND gate with k inputs is called and ANDk gate (e.g., an AND2, AND3, etc).Can implement AND3 with multiple AND2 gates, or with single transistor circuit.AND/OR are associative and commutative -- combine in any order.NAND and NOR are not associative.Jim Conrad’s example:NAND(NAND(0,0), 1) = NAND(1, 1) = 0NAND(0, NAND(0,1)) = NAND(0, 0) = 1
16Logical Completeness Can implement ANY truth table with AND, OR, NOT. 1AND combinations that yield a "1" in the truth table.Put a “bubble” (inverter) for every 0, a straight-in for every 1 in a row2. OR the results of the AND gates.If there are N 1’s, there will be N and gates; the or gate will have N inputsNote the use of the bubbles (NOT) in the input.
17invert inputs and output. DeMorgan's LawConverting AND to OR (with some help from NOT)Consider the following gate:To convert AND to OR(or vice versa),invert inputs and output.AB1If there's time, perhaps discuss how all gates can be implemented with NAND (or NOR).Therefore, you can implement any truth table using only NAND (or NOR) gates.Same as A OR B!
18SummaryMOS transistors are used as switches to implement logic functions.N-type: connect to GND, turn on (with 1) to pull down to 0P-type: connect to +2.9V, turn on (with 0) to pull up to 1Basic gates: NOT, NOR, NANDLogic functions are usually expressed with AND, OR, and NOTProperties of logic gatesCompletenesscan implement any truth table with AND, OR, NOTDeMorgan's Lawconvert AND to OR by inverting inputs and output