Introduction to Computer Engineering CS ECE 252 Spring 2007 Prof Mark D Hill Computer Sciences Department University of Wisconsin Madison Chapter 3 Digital Logic Structures Slides based on set prepared by Gregory T Byrd North Carolina State University Copyright The McGraw Hill Companies Inc Permission required for reproduction or display Transistor Building Block of Computers Microprocessors contain millions of transistors Intel Pentium II 7 million Compaq Alpha 21264 15 million Intel Pentium III 28 million Logically each transistor acts as a switch Combined to implement logic functions AND OR NOT Combined to build higher level structures Adder multiplexer decoder register Combined to build processor LC 3 3 3 Copyright The McGraw Hill Companies Inc Permission required for reproduction or display Simple Switch Circuit Switch open No current through circuit Light is off Vout is 2 9V Switch closed Short circuit across switch Current flows Light is on Vout is 0V Switch based circuits can easily represent two states on off open closed voltage no voltage 3 4 Copyright The McGraw Hill Companies Inc Permission required for reproduction or display 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 Gate 1 Gate 0 Terminal 2 must be connected to GND 0V 3 5 Copyright The McGraw Hill Companies Inc Permission required for reproduction or display P type MOS Transistor P type is complementary to N type 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 Gate 0 Terminal 1 must be connected to 2 9V 3 6 Copyright The McGraw Hill Companies Inc Permission required for reproduction or display 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 1 1V for purposes of illustration we ll use 2 9V 3 7 Copyright The McGraw Hill Companies Inc Permission required for reproduction or display 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 3 8 Copyright The McGraw Hill Companies Inc Permission required for reproduction or display Inverter NOT Gate Truth table In Out 0 V 2 9 V 2 9 V 0V In Out 0 1 1 0 3 9 Copyright The McGraw Hill Companies Inc Permission required for reproduction or display NOR Gate Note Serial structure on top parallel on bottom A B C 0 0 1 0 1 0 1 0 0 1 1 0 3 10 Copyright The McGraw Hill Companies Inc Permission required for reproduction or display OR Gate A B C 0 0 0 0 1 1 1 0 1 1 1 1 Add inverter to NOR 3 11 Copyright The McGraw Hill Companies Inc Permission required for reproduction or display NAND Gate AND NOT Note Parallel structure on top serial on bottom A B C 0 0 1 0 1 1 1 0 1 1 1 0 3 12 Copyright The McGraw Hill Companies Inc Permission required for reproduction or display AND Gate A B C 0 0 0 0 1 0 1 0 0 1 1 1 Add inverter to NAND 3 13 Copyright The McGraw Hill Companies Inc Permission required for reproduction or display Basic Logic Gates 3 14 Copyright The McGraw Hill Companies Inc Permission required for reproduction or display 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 3 15 Copyright The McGraw Hill Companies Inc Permission required for reproduction or display Practice Implement a 3 input NOR gate with CMOS 3 16 Copyright The McGraw Hill Companies Inc Permission required for reproduction or display Logical Completeness Can implement ANY truth table with AND OR NOT A B C D 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 1 AND combinations that yield a 1 in the truth table 2 OR the results of the AND gates 3 17 Copyright The McGraw Hill Companies Inc Permission required for reproduction or display Practice Implement the following truth table A B C 0 0 0 0 1 1 1 0 1 1 1 0 3 18 Copyright The McGraw Hill Companies Inc Permission required for reproduction or display DeMorgan s Law Converting AND to OR with some help from NOT Consider the following gate A B A B A B A B 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 0 1 1 1 0 0 0 1 To convert AND to OR or vice versa invert inputs and output Same as A B 3 19 Copyright The McGraw Hill Companies Inc Permission required for reproduction or display Summary MOS transistors are used as switches to implement logic functions N type connect to GND turn on with 1 to pull down to 0 P type connect to 2 9V turn on with 0 to pull up to 1 Basic gates NOT NOR NAND Logic functions are usually expressed with AND OR and NOT Properties of logic gates Completeness can implement any truth table with AND OR NOT DeMorgan s Law convert AND to OR by inverting inputs and output 3 20 Copyright The McGraw Hill Companies Inc Permission required for reproduction or display Building Functions from Logic Gates We ve already seen how to implement truth tables using AND OR and NOT an example of combinational logic Combinational Logic Circuit output depends only on the current inputs stateless Sequential Logic Circuit output depends on the sequence of inputs past and present 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 3 21 Copyright The McGraw Hill Companies Inc Permission required for reproduction or display Decoder n inputs 2n outputs exactly one output is 1 for each possible input pattern 2 bit decoder 3 22 Copyright The McGraw Hill Companies Inc Permission required for reproduction or display Multiplexer MUX n bit selector and 2n inputs one output output equals one of the inputs depending on selector 4 to 1 MUX 3 23 Copyright The McGraw Hill Companies Inc Permission required for reproduction or display Full Adder Add two bits and carry in produce one bit sum and carry out A …