dna fundamentals of digital logic
TRANSCRIPT
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GoalsUnderstand basics of digital circuits
transistorsboolean logic → logic gatesgates → integrated circuitscountersfeedback – keeping bits in check
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BackgroundVoltage: difference of potentials.
Vcc – ground (=0).Volts (V)
Current: flow of electrons.Amperes (A)
Ohm’s law: U = RIDissipated power: P = UI = RI2 = U2/R
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Typical ChipsOperate on low voltage (5V, less for processors) – see power dissipation.Always 2 lines
ground (0V)power (5V)
Diagrams usually omit ground and power.
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Transistor Basic buildingblock of digitalcircuits
Acts like a switch.emitter
base
collector
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Transistor (NPN)P doped siliconelectron “holes”anodeN doped silicon
surplus of electronscathode
(wikipedia fig.)
Different technologiesbased on the samebasic principle.
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How Are They Made?
sand
pure siliconwith perfectcrystalline structure
slice into wafers
photo-lithography
doping materials (N/P)metal (copper/gold)
cut
connect &package
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Boolean AlgebraMathematical basis for digital circuits.From boolean functions to gates.Basic functions: and, or, not.In practice, cheaper to have nand & nor.
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Example: Not
You also have nor in the book.
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GatesPrimitive boolean functions.Level of abstraction on IC.
Symbols used in circuits.
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Logic Gate TechnologyTransistor-transistor technology (TTL)
connect directly gates together to form boolean functions
and function
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Example
¬Y
Z nor ¬Y
X and (Z nor ¬Y)
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Design of FunctionsFind a boolean expression that does what you need
and feed it to a tool that optimizes it to minimize the number of gates.
Come up with the truth table of your functionwhich is converted to a boolean function.
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Truth Table
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Combinatorial Circuits
Outputs = function(inputs)change outputs only when inputs changesneed states to perform sequences of operations without sustained inputs
maintain statesuse a clock
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Maintaining StatesFlip-flop example
?
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T-Flip-Flop
clock
input output
¬output
symboltruth table
Key: feedback
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To KnowCan occur on leading or falling edge of the clock signal.Variants of flip-flops.Transition diagrams used to visualize the function.Key: feedback to “keep” the bits.Simple not loop = base for memory bit (cache).
RAM: simpler with a “condensator”more compact but needs to be refreshed
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Binary CountersCount input pulses.Output = binary number.The IC keeps previous states
→ combines with new inputs to get new output→ combination = boolean function
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Clocks and Sequences
Input: codedbinary n.
Output:line n is set.
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Clocks and Sequences12
3
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Software vs. HardwareSoftware: iterations common.
Avoid replication.
Hardware: replication easier & faster.Iteration clumsier.
Major difference: parallelism.
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Practical ConcernsPower
consumption: how to feeddissipation P=CFV2 (C: capacitance, F: frequency)how not to burn
Timing – gates need time to settle.Clock synchronization.
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Clock Skew
Signals need time to propagate.Local clocks are used on largersystems → need to synchronizethem.The speed of light is too slow.
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Levels of Abstraction