Engineering Lecture 3 Digital Electronics by Jaroslaw Karcz.
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Transcript of Engineering Lecture 3 Digital Electronics by Jaroslaw Karcz.
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Engineering Lecture 3Engineering Lecture 3
Digital ElectronicsDigital Electronics
by Jaroslaw Karcz
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1. BASIC LOGIC CONCEPTS
2. COMBINATIONAL LOGIC
3. SEQUENTIAL LOGIC
OverviewOverview
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Analogue SignalsAnalogue Signals
1.1. BASIC LOGIC CONCEPTSBASIC LOGIC CONCEPTS
• Representation of a quantity that varies over a continuous range of values e.g. sound, light, temperature, and pressure
• These may be represented electrically by an analogue voltage/current
• A device that is used to convert an analogue signal into an analogue voltage or current is known as a transducer
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Digital SignalsDigital Signals
• Representation of a quantity that varies in discrete steps over a range of values
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Logic StatesLogic States• Digital Electronics = circuits in which only 2 states possible at any point e.g. transistor can either be in saturation or be non-conducting
• Choose to talk about voltages, calling a level HIGH or LOW
• Depending on context, can be represented as following for example:
one bit (binary digit) of a number (0 or 1) whether switch is opened or closed whether signal is present or absent some analogue level is above/below some preset limit (threshold) whether some event has occurred yet whether some action should be performed etcetera….
• HIGH and LOW states represent the TRUE and FALSE states of Boolean logic, in some predefined way
• Digital Electronics = circuits in which only 2 states possible at any point e.g. transistor can either be in saturation or be non-conducting
• Choose to talk about voltages, calling a level HIGH or LOW
• Depending on context, can be represented as following for example:
one bit (binary digit) of a number (0 or 1) whether switch is opened or closed whether signal is present or absent some analogue level is above/below some preset limit (threshold) whether some event has occurred yet whether some action should be performed etcetera….
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Analogue to Digital ConversionAnalogue to Digital Conversion
• In real world, signals appear in analogue form.
• It is often desirable to convert continuous (analogue) data to digital (discrete) form
• Conversion to digital format requires definition of threshold values
e.g.
in electronics, the voltage levels corresponding to HIGH or LOW are allowed to fall in some range
• Typical LOW- and HIGH-state output voltages are usually within
a tenth of a volt of 0 and +5 volts, respectively
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2.2. COMBINATORIAL LOGICCOMBINATORIAL LOGIC
Circuits composed of combinations of logic gates,
with NO FEEDBACK from outputs to inputs
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Gates and Truth Tables - Gates and Truth Tables - BASICBASIC
The AND gate
IEEE /ANSI SymbolOlder (Mil-Spec) Symbol
111
001
010
000
Output FInput YInput X
• Output is HIGH (1) if and only if all inputs are HIGH (1).
• If any input(s) are LOW (0), the output is guaranteed to be in a LOW state
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..\Pictures\Digital Gates\or.gif
The OR gate
Gates and Truth TablesGates and Truth Tables
111
101
110
000
Output FInput YInput X
• Output will be HIGH (1) if any of the inputs are HIGH (1)
• Output goes LOW (0) if and only if all inputs are LOW (0).
The OR gate
Gates and Truth TablesGates and Truth Tables
111
101
110
000
Output FInput YInput X
The OR gate
Gates and Truth TablesGates and Truth Tables
• Output will be HIGH (1) if any of the inputs are HIGH (1)
• Output goes LOW (0) if and only if all inputs are LOW (0).
111
101
110
000
Output FInput YInput X
The OR gate
Gates and Truth Tables - Gates and Truth Tables - BASICBASIC
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• Whatever logical state is applied to the input, the opposite state will
appear at the output
The NOT gate (inversion)
Gates and Truth Tables - Gates and Truth Tables - BASICBASIC
01
10
Output FInput X
Also denoted as X’ – inverse of X
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Gates and Truth Tables - Gates and Truth Tables - DERIVEDDERIVEDThe NAND gate
011
101
110
100
Output FInput YInput X • With the gate shown above, both inputs must have logic 1 signals applied to them in order for the output to be a logic 0.
• With either input at logic 0, the output will be held to logic 1.
(derived from AND & NOT gates)
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Gates and Truth Tables - Gates and Truth Tables - DERIVEDDERIVED
The NOR gate (same principle applies)
011
001
010
100
Output FInput YInput X
•NOR gate is an OR gate with the output inverted
•Where OR gate allows the output to be HIGH (1), if any input is true, the NOR gate inverts this and forces the output to logic 0 (LOW).
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Gates and Truth Tables – Gates and Truth Tables – still more??still more??
The XOR gate
The XNOR gate
011
101
110
000
Output FInput YInput X
111
001
010
100
Output FInput YInput X
• Output HIGH when inputs are inverses of each other
• Output HIGH when inputs are exactly the same
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3.3. SEQUENTIAL LOGICSEQUENTIAL LOGIC
• Use of devices in such a manner that the new state of an output may depend not only on the existing state of its inputs, but also on previous conditions imposed upon the inputs. In other words, capacity for MEMORY
• This allows for construction of devices such as:
Counters
Arithmetic Accumulators
Frequency Dividers, etc.
• The most fundamental unit of sequential logic is the FLIP-FLOP
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Operation of NAND Gate Flip-Flop
“Setting the latch”
The time sequence displays the conditions under which the set (S) and reset (R) inputs cause a state change, and those for which they remain unaltered.
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D Flip-flop Divide-by-2-Circuit
Ripple-Down Counter
Flip-flopsFlip-flops
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Flip-flopsFlip-flops
• Q+ indicates the value of Q after the next clock pulse (output only changes upon
a particular state of the clock pulse) – here PGT
• If J and K are different, Q takes on the value of J
• If J and K are both 0, Q remains unchanged
• If J and K are both 1, Q changes to its inverse (it "toggles")
• Information from J and K is read in on the rising edge of the clock, and is
translated into action at the Q outputs on the FALLING edge of the clock
Truth TableJ-K Flip-flop
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Applications of Flip-flopsApplications of Flip-flops
T-Flip Flop
Synchronous Counter (created through use of T-flip flop : slightly modified J-K Flip-Flop)
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A circuit which can store temporarily all bits of a binary number
(a typical personal computer will have several 16-bit and 32-bit data registers in its arithmetic unit)
Applications of Flip-flopsApplications of Flip-flops
Symbol“Anatomy” of Data Register composed of D Flip-flops
3-bit register
Data Register