! Logically, each transistor acts as a switch! Combined to implement logic functions (gates) n AND, OR, NOT
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1 Computing Layers Chapter 3 Digital Logic Structures Problems Algorithms Language Instruction Set Architecture Microarchitecture Original slides from Gregory Byrd, North Carolina State University Modified slides by Chris Wilcox, Colorado State University Circuits Devices 2 Transistor: Building Block of Computers! Microprocessors contain lots of transistors Intel 8086 (1978): 29 thousand Intel (1982): 55 thousand Intel (1985): 275 thousand Intel (1989): 1.1 million Intel Pentium (1993): 3.1 million Intel Pentium II (1998): 7.5 million Intel Pentium III (2001): 45 million Intel Pentium 4 (2006): 184 million Intel Core 2 Duo (2006): 291 million Intel Quad Core i7 (2011): 1.1 billion Intel 8-core Xeon (2012): 2.3 billion 3 Transistor: Building Block of Computers! Logically, each transistor acts as a switch! Combined to implement logic functions (gates) AND, OR, NOT! Combined to build higher-level structures Adder, multiplexer, decoder, register, memory Adder, multiplier! Combined to build simple processor LC-3 4 1
2 Simple Switch Circuit! Switch open: Open circuit, no current Light is off V out is +2.9V! Switch closed: Short circuit across switch, current flows Light is on V out is 0V Switch-based circuits can easily represent two states: on/off, open/closed, voltage/no voltage. 5 n-type MOS Transistor! MOS = Metal Oxide Semiconductor two types: n-type and p-type! n-type when 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) Terminal #2 must be connected to GND (0V). Gate = 1 Gate = 0 6 p-type MOS Transistor! p-type is complementary to n-type when Gate has positive voltage, open circuit between #1 and #2 (switch open) Gate = 1 when Gate has zero voltage, short circuit between #1 and #2 (switch closed) Physical Transistor Gate = 0 Terminal #1 must be connected to +2.9V
3 Transistor Output (Ideal) Transistor Output (Actual) Logic analyzer view of waveforms Actual waveform is not ideal! 9 10 Logic Gates! Use switch behavior of MOS transistors to implement logical functions: AND, OR, NOT.! Digital symbols: recall that we assign a range of analog voltages to each digital (logic) symbol assignment of voltage ranges depends on electrical properties of transistors being used! typical values for "1": +5V, +3.3V, +2.9V! from now on we'll use +2.9V CMOS Circuit! Complementary MOS! Uses both n-type and p-type MOS transistors p-type! Attached to + voltage! Pulls output voltage UP when input is zero n-type! Attached to GND! Pulls output voltage DOWN when input is one! For all inputs, make sure that output is either connected to GND or to +, but not both!
4 Inverter (NOT Gate) NOR Gate (OR-NO) In Out 0 V 2.9 V 2.9 V 0 V In Out Note: Serial structure on top, parallel on bottom OR Gate NAND Gate (AND-NOT) Add inverter to NOR. 15 Note: Parallel structure on top, serial on bottom
5 AND Gate Basic Logic Gates Add inverter to NAND DeMorgan's Law! Converting AND to OR (with some help from NOT)! Consider the following gate: A B A B A B A B To convert AND to OR (or vice versa), invert inputs and output. More 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.! Can implement with multiple two-input gates, or with single CMOS circuit. Same as A OR B!
6 Summary Building Functions from Logic Gates! MOS transistors are used as switches to implement logic functions. n-type: connect to GND, turn on (1) to pull down to 0 p-type: connect to +2.9V, turn on (0) to pull up to 1! Basic gates: NOT, NOR, NAND! Combinational Logic Circuit output depends only on the current inputs stateless! Sequential Logic Circuit output depends on the sequence of inputs (past and present) Logic functions are usually expressed with AND, OR, and NOT! DeMorgan's Law Convert AND to OR (and vice versa) by inverting inputs and output stores information (state) from past inputs! We'll first look at some useful combinational circuits, then show how to use sequential circuits to store information
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