ECE Digital Logic Lecture 2. Digital Design Circuit Types: Combinational vs. Sequential

Transcription

1 ECE 74 - Digital Logic Lecture Circuit Types: Combinational vs. equential Lecture Transistors, witches, CMO Basic Logic Gates Boolean Equations Truth Table: w/o time or previous values Circuit Components: Historical Perspective Transistors as witches: Binary witch = 0 = (a) Two states of a switch The evolution of switches: Relays (930s), vacuum tubes (940s), discrete transistors (950s), and integrated circuits (ICs) containing transistors (960s--present). IC s originally held about ten transistors; now they can hold more than a billion. (b) ymbol for a switch 3 4 Transistors as witches: Light controlled be a witch Transistors as witches: Basic Functions (AND/OR) Battery L Light (a) imple connection to a battery Power supply L (b) Using a ground connection as the return path 5 6

2 CMO transistors: (a) transistor on silicon, (b) nmo transistor symbol with indication of conducting when gate=, (c) pmo transistor symbol conducts when gate=0. CMO transistor operation analogy -- A person may not be able to cross a river, until just enough stepping stones are attracted into one pathway. Likewise, electrons can t cross the channel between source and drain, until just enough electrons are attracted into the channel. 7 8 Circuit Logic: Historical Perspective Having the right building blocks can make all the difference when building things. hannon applied Boolean algebra to switch-based circuits, providing a formal basis to digital circuit design. 9 0! +y y Everyday Boolean Logic: I ll(i) go to lunch if Mary(m) goes OR John(j) goes, AND ally(s) does not go. Which answer correctly represents the statement above: A) j = (i + m)(s) B) i = (j)(m +!s) C) i = (m + j) (!s) Warning: real AND and OR gates aren t actually built this way, but rather in a more comple manner

3 Everyday Boolean Logic: I ll(i) go to lunch if Mary(m) goes OR John(j) goes, AND ally(s) does not go. Will you go to lunch if: m =, j = 0, and s =? A) No (i = 0) B) Yes (i = ) Converting English Problem to Boolean Logic: A fire sprinkler system should spray water if high heat is sensed and the system is set to enabled. Identify and label variables: h represents high heat is sensed e represents enabled F represents spraying water Write Boolean Equation epressing functionality described F = h AND e 3 4 AND gates n n + OR gates n n NOT gate Three-input AND and OR. 5 6 : Inverter : Inverter Inverter conduction paths when: (a) the input is 0, and (b) the input is. Inverter timing diagram. 7 8

4 : OR Gate : OR Gate OR gate conduction paths when: (a) one input is, and (b) both inputs are 0. OR gate timing diagram. 9 0 : AND Gate : AND Gate 0 AND gate conduction paths when: (a) all inputs are, and (b) any input is 0. y 0 F 0 time AND gate timing diagram. : Converting Boolean Equations to Circuits Building the circuit for F = a AND NOT (b OR NOT (c)): (a) partial, (b) complete. Converting Boolean equations to circuits. 3 4

5 Using multiple-input AND gates: (a) using -input AND gates, (b) using a 3-input AND gate. 5