1ECE 274 - Digital LogicLecture 2 Lecture 2 Transistors, Switches, CMOS Basic Logic Gates Boolean Equations2Digital DesignCircuit Types: Combinational vs. SequentialTruth Table: w/o time or previous values3Digital DesignCircuit Components: Historical PerspectiveThe evolution of switches: Relays (1930s), vacuum tubes (1940s), discrete transistors (1950s), and integrated circuits (ICs) containing transistors (1960s--present). IC’s originally held about ten transistors; now they can hold more than a billion.4x 1 = x 0 = (a) Two states of a switchS x (b) Symbol for a switch Digital DesignTransistors as Switches: Binary Switch5(a) Simple connection to a batteryS x (b) Using a ground connection as the return pathL Battery Light x Power supplyS L Digital DesignTransistors as Switches: Light controlled be a Switch6Digital DesignTransistors as Switches: Basic Functions (AND/OR)7Digital DesignCombinational Logic DesignCMOS transistors: (a) transistor on silicon, (b) nMOS transistor symbol with indication of conducting when gate=1, (c) pMOS transistor symbol conducts when gate=0.8Digital DesignCombinational Logic DesignCMOS 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. 9Digital DesignCombinational Logic DesignHaving the right building blocks can make all the difference when building things.10Digital DesignCircuit Logic: Historical PerspectiveShannon applied Boolean algebra to switch-based circuits, providing a formal basis to digital circuit design.11Digital DesignCombinational Logic Design: Basic Logic GatesWarning: real AND and OR gates aren’tactually built this way, but rather in a more complex manner!xx+yxy12Digital DesignCombinational Logic Design: Basic Logic Gates Everyday Boolean Logic: I’ll(i) go to lunch if Mary(m) goes OR John(j) goes, AND Sally(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)13Digital DesignCombinational Logic Design: Basic Logic Gates Everyday Boolean Logic: I’ll(i) go to lunch if Mary(m) goes OR John(j) goes, AND Sally(s)does not go.Will you go to lunch if: m = 1, j = 0, and s = 1?A) No (i = 0)B) Yes (i = 1)14Digital DesignCombinational Logic Design: Basic Logic Gates 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:hrepresents “high heat is sensed”erepresents “enabled”Frepresents “spraying water” Write Boolean Equation expressing functionality describedF = h AND e 15Three-input AND and OR.Digital DesignCombinational Logic Design: Basic Logic Gates16x 1 x 2 x 1 x 2 + AND gates OR gatesx x x 1 x 2 x n x 1 x 2 …x n + + + NOT gatex 1 x 2 x 1 x 2 ⋅x 1 x 2 x n x 1 x 2 …x n ⋅⋅⋅Digital DesignCombinational Logic Design: Basic Logic Gates17Digital DesignCombinational Logic Design: InverterInverter conduction paths when: (a) the input is 0, and (b) the input is 1.18Digital DesignCombinational Logic Design: InverterInverter timing diagram.19Digital DesignCombinational Logic Design: OR GateOR gate conduction paths when: (a) one input is 1, and (b) both inputs are 0.20Digital DesignCombinational Logic Design: OR GateOR gate timing diagram.21Digital DesignCombinational Logic Design: AND GateAND gate conduction paths when: (a) all inputs are 1, and (b) any input is 0.22Digital DesignCombinational Logic Design: AND GateAND gate timing diagram.xFtime1010y1023Digital DesignCombinational Logic DesignBuilding the circuit for F = a AND NOT (b OR NOT (c)): (a) partial, (b) complete.24Digital DesignCombinational Logic Design: Converting Boolean Equations to CircuitsConverting Boolean equations to circuits.25Digital DesignCombinational Logic DesignUsing multiple-input AND gates: (a) using 2-input AND gates, (b) using a 3-input AND