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Lecture Introduction to computing systems: Chapter 3 - Yale N. Patt, Sanjay J. Patel

Chapter 3 - Digital logic structures. This chapter presents the following content: Electronic ones and zeros, transistors, CMOS transistors, inverter gate, NOR gate, NOR gate - Operation, OR gate, NAND & AND Gates, logic gates & symbols, De Morgan’s Law,.and other contents. | Chapter 3 Digital Logic Structures Transistors Logic gates & Boolean logic Combinational logic Storage Elements Memory Electronic ones and zeros An electronic switch like a light switch or faucet switches between insulator (open circuit) and conductor (closed circuit) We can call the presence of a voltage “1” and its absence “0” 3 - Transistors An electronic switch that is open or closed between the source and the drain depending on the voltage on the gate. 3 - A B G N Open (insulating) if gate is “off” = 0 Closed (conducting) if gate is “on” = 1 P Open (insulating) if gate is “on” = 1 Closed (conducting) if gate is “off” = 0 A B G CMOS Transistors CMOS = Complementary Metal-Oxide Semiconductor Standard type for digital applications Two versions: P-type (positive) and N-type (negative) P and N-type transistors operate in inverse modes 3 - 2.9 v 0 v out in Inverter Gate When the input is on (in = high voltage), the P-type transistor is open and the N-type is closed, so the output is off (out = low voltage). Vice-versa: when the Input is off (in = low voltage), the output is connected to the high voltage. P N 3 - NOR Gate C A B 2.9 v 0 v 0 v P N P N 3 - NOR Gate - Operation 2.9 v 0 v 0 v P N P 0 v 0 v 2.9 v N N 0 v 0 v P N P N 2.9 v 2.9 v 0 v 0 v 2.9 v 0 v 0 v P N 2.9 v 2.9 v 0 v P 3 - OR Gate D A B C = a NOR gate followed by an inverter 3 - NAND & AND Gates A B C D 3 - Logic Gates & Symbols Note that gates can have more than 2 inputs. 3 - De Morgan’s Law not(A and B) = (not A) or (not B) not(A or B) = (not A) and (not B) = = 3 - Completeness It can be shown that any truth table (i.e. any binary function of two variables) can be reduced to combinations of the AND & NOT functions, or of the OR & NOT functions. This result extends also to functions of more than two variables In fact, it turns out to be convenient to use a basic set of three logic gates: AND, OR & NOT or NAND, NOR & NOT 3 - Representation of Logic Functions A | Chapter 3 Digital Logic Structures Transistors Logic gates & Boolean logic Combinational logic Storage Elements Memory Electronic ones and zeros An electronic switch like a light switch or faucet switches between insulator (open circuit) and conductor (closed circuit) We can call the presence of a voltage “1” and its absence “0” 3 - Transistors An electronic switch that is open or closed between the source and the drain depending on the voltage on the gate. 3 - A B G N Open (insulating) if gate is “off” = 0 Closed (conducting) if gate is “on” = 1 P Open (insulating) if gate is “on” = 1 Closed (conducting) if gate is “off” = 0 A B G CMOS Transistors CMOS = Complementary Metal-Oxide Semiconductor Standard type for digital applications Two versions: P-type (positive) and N-type (negative) P and N-type transistors operate in inverse modes 3 - 2.9 v 0 v out in Inverter Gate When the input is on (in = high voltage), the P-type transistor is open and the N-type is closed, so the