Last week Processor (CPU) made of millions of transistors - PDF document

10/19/2009 Last week  Processor (CPU) made of millions of transistors  Integrated circuits allow small powerful CPUs  Control Unit, ALU, Registers, Bus, Cache  Co- and multi-core processors  Moore’s law: transistors on chip double in 2 yrs 1

10/19/2009 This week  How are transistors used to process data?  Combining transistors  Logic gates  The NAND gate  Digital circuits  Adding two bits Transistors control electricity  Control current (0 or 1) via base voltage (0 or 1)  An open transistor lets current flow through  NPN: open only if base is on (1)  PNP: open only if base is off (0) 2

10/19/2009 Transistors control electricity  Control current (0 or 1) via base voltage (0 or 1)  An open transistor lets current flow through  NPN: open only if base is on (1)  PNP: open only if base is off (0) Transistors control electricity  Control current (0 or 1) via base voltage (0 or 1)  An open transistor lets current flow through  NPN: open only if base is on (1)  PNP: open only if base is off (0) 3

10/19/2009 Combining transistors The NOT gate  Can build a NOT gate using 2 transistors  If A is 0 then X is 1  If A is 1 then X is 0 Combining transistors The NOT gate  Can build a NOT gate using 2 transistors  If A is 0 then X is 1  If A is 1 then X is 0 4

10/19/2009 Combining transistors The NOT gate  Can build a NOT gate using 2 transistors  If A is 0 then X is 1  If A is 1 then X is 0 Logic gates NOT T gate  On only when input is off  X = NOT A 5

10/19/2009 Logic gates AND gate  On when both inputs are on  X = AND A, B Logic gates OR gate  On when either input is on  X = OR A, B 6

10/19/2009 Logic gates NAND D gate  NOT AND: On unless both inputs are on  X = NAND A, B Logic gates NOR gate  NOT OR: On when neither input is on  X = NOR A, B 7

10/19/2009 Logic gates XOR gate  Exclusive OR: On when only one input is on  X = XOR A, B Logic gates XNOR OR gate  Exclusive NOT OR: On when both inputs equal  X = XNOR A, B 8

10/19/2009 Logic gates The NAND gate Not ot in the exam Buildi ding g a NA NAND  Can build a NAND gate using 4 transistors 9

10/19/2009 The NAND gate Not ot in the exam Buildi ding ng a NAND  Can build a NAND gate using 4 transistors The NAND gate Not ot in the exam Building lding a NAND  Can build a NAND gate using 4 transistors 10

10/19/2009 The NAND gate Not ot in the exam Building lding a NAND  Can build a NAND gate using 4 transistors The NAND gate Not ot in the exam Building lding a NAND  Can build a NAND gate using 4 transistors 11

10/19/2009 The NAND gate Funct ction ional al Comp mplet eten eness ess  Can build a NAND gate using 4 transistors  NAND & NOR are simplest 2-input gates  NAND is functionally complete (so is NOR)  It can be used to build all the other gates  e.g. an AND gate  In practice, processors contain just NAND gates The NAND gate Funct ction ional al Comp mplet eten eness ess NOT A = NAND A, A AND A, B = NOT (NAND A, B) OR A, B = NAND (NOT A), (NOT B) XOR A, B = OR (AND (NOT A), B), (AND A (NOT B)) 12

10/19/2009 Digital circuits The Half Ad Adder er  Adds two bits ( A and B) together (sum S)  Carry bit ( C) indicates if sum is more than one bit Digital circuits The Half Ad Adder  Sum S = XOR A, B  Carry C = AND A, B 13

10/19/2009 Digital circuits The Full Ad Adder  When adding column of binary digits may get a carry bit from the previous column  Adds together two bits ( A and B) and a carry in bit C1  Carry-out C2 indicates if sum is more than one bit Digital circuits Not ot in the exam The Full Ad Adder Sum S = XOR (XOR A, B), C Carry-out C2 = OR (AND A, B), (AND C1, (XOR A, B)) 14

10/19/2009 Digital circuits Arithm thmetic etic-Log ogic c Unit (ALU)  ALU contains circuits for different operations  Arithmetic operations  Addition (Full adder for each binary column)  Subtraction, multiplication, division  Logical operations  AND, OR, NOT, ...  Bitwise operations  Shifts, rotations Summary  Logic gates are built out of transistors  There are many different logic gates  NAND is functionally complete  Digital circuits process data using gates  Half and full adder  Reading: Brookshear §1.1, White p.68- 69  http://en.wikipedia.org/wiki/Logic_gate 15