3
Logic Values
•Logic values = {0, 1}
•A logic value, 0 or 1, is called as BInary DigiT or BIT.
•Physical states representing bits in digital
technologies:
4
Encoding Bits
•Information can be encoded using:
–Current, Voltage, Phase, Frequency
•Digital systems use two voltage levelsvoltage levels for encoding
bits.
–LOW: A signal close to the GND
–HIGH: A signal close to the VCC
5
Encoding Bits
•Positive logic
–High: 1 and Low: 0
–Our convention in this course
•Negative logic
–High: 0 and Low: 1
6
Logic Gates
•Gates are basic digital devices.
–A gate takes one or more inputs and produces an output.
–Inputs are either 0 or 1.
•Although they may have very different values of voltage.
–Output is either 0 or 1.
–A logic gate’s operation is fully described by a truth table.
7
Logic Families – What is inside of a logic gate?
•A logic family is a collection of different integrated-
circuit chips that have similar input, output, and
internal circuit characteristics, but that perform
different logic functions.
•Logic gates are made from transistors.
–TTL (Transistor-Transistor Logic) family gates are made from
bipolar transistors.
–CMOS (Complementary Metal Oxide Semiconductor) family
logic gates are made from MOS transistors.
8
MOS Transistors – N-type MOSFET
•OFF (open circuit) : when gate is logical zero
•ON (short circuit) : when gate is logical one
• Passes a good logical zero
• Degrades a logical one
9
MOS Transistors – P-type MOSFET
•OFF (open circuit) : when gate is logical one
•ON (short circuit) : when gate is logical zero
• Passes a good logical one
• Degrades a logical zero
10
CMOS Logic Gates
11
Inverter
12
Inverter
13
NAND – Not AND
14
NAND
15
NOR – Not OR
16
Non-inverting Buffer
17
AND Gate
18
OR Gate
19
CMOS Electrical Characteristics
•Digital analysis works only if circuits are operated in
specs:
–Power supply voltage
–Temperature
–Input-signal quality
–Output loading
•Must do some “analog” analysis to prove that circuits
are operated in spec.
–Fan-out specs
–Timing analysis (setup and hold times)
– Analysis involves only consequences of V = IR (static)
and q = CV (dynamic)
22
Logic Levels
•Typical transfer characteristic of a CMOS inverter:
–LOW input level: < 2.4 Volt
–HIGH input level: > 2.6 Volt
•Transfer characteristic depends on power-supply
voltage, temperature and output loading.
23
Logic Levels
•Should use more conservative specifications for LOW
and HIGH
–V
ILmax
: max input voltage guaranteed to be recognized as a LOW level
•30% of V
CC
–V
OLmax
: max output voltage in the LOW level
•GND + 0.1 V
–V
OHmin
: min output voltage in the HIGH level
•V
CC
– 0.1 V
–V
IHmin
: min input voltage guaranteed to be recognized as a HIGH level
•70% of V
CC
24
Logic Levels
V
IHminV
OHmin
V
ILmaxV
OLmax
25
DC Noise Margins
•DC noise margin is a measure of how much noise it
takes to corrupt a worst-case output voltage into a
value that may not be recognized properly by an input.
–Noise Margin Low = V
ILmax
– V
OLmax
= 1.35
– 0.1 = 1.25 V
–Noise Margin High = V
OHmin
– V
IHmin
= 4.4
– 3.15 = 1.25 V
26
Input Currents
•CMOS gate inputs consume very little current, only the
leakage current of the two transistors’ gates.
–I
IH
: max current that flows into the input in HIGH state
–I
IL
: max current that flows into the input in LOW state
27
DC Output Loading
•An output must sink
current from a load when
the output is in the LOW
state.
•An output must source
current to a load when
the output is in the HIGH
state.
28
DC Output Loading Specs
•V
OLmax
and V
OHmin
are specified for certain output-current
values, I
OLmax
and I
OHmax
.
–I
OLmax
: max current that output can sink in the LOW state while
still maintaining an output voltage no greater than V
OLmax
–I
OHmax
: max current that output can source in the HIGH state
while still maintaining an output voltage no less than V
OHmin
29
DC Output Loading - Output-voltage Drops
•Resistance of “off” transistor is > 1 Megaohm, but
resistance of “on” transistor is nonzero,
–Voltage drops across “on” transistor, V = IR
•For “CMOS” loads, current and voltage drop are
negligible.
•For TTL inputs, LEDs, terminations, or other resistive
loads, current and voltage drop are significant and must
be calculated.
•If too much load, output voltage will go outside of valid
logic-voltage range.
–V
OHmin
, V
IHmin
–V
OLmax
, V
ILmax
30
Fan-in
•The number of inputs that a gate can have in a
particular logic family is called the logic family’s fan-in.
–You could design a CMOS NAND or NOR gates with a very
large number of inputs.
–In practice, additive “on” resistance of series transistors
limits the fan-in of CMOS gates – Lower speed.
•Max fan-in = 4 for NOR, 6 for NAND
3-input NAND gate
7-input NAND gate using
4-input NAND gates
31
Fan-out
•The fan-out of a gate is the number of inputs that the
gate can drive without exceeding its worst-case loading
specifications.
–Characteristics of the gate’s output
–Characteristics of the inputs that it is driving
•DC fan-out: The number of inputs that an output can
drive with the output in a constant state (high or low).
•AC fan-out: The ability of an output to charge or
discharge the stray capacitance associated with the
inputs that it drives.
–If the capacitance is too large, the transition from low to high
(or vice versa) may be too slow, causing improper system
operation.
32
DC Fan-out Calculation
•LOW state: The sum of the I
IL
values of the driven
inputs may not exceed I
OLmax
of the driving output.
•HIGH state: The sum of the I
IH
values of the driven
inputs may not exceed I
OHmax
of the driving output.
Low State Fan-out=
20 μA/1 μA= 20
High State Fan-out=
20 μA/1 μA= 20
33
AC Loading
•AC loading has become a critical design factor as
industry has moved to pure CMOS systems.
–CMOS inputs have very high impedance, DC loading is
frequently negligible (low fan-outs).
–CMOS inputs and related packaging and wiring have significant
capacitance.
–Time to charge and discharge capacitance is a major
component of delay.
•Gate’s speed and power consumption depend on the AC
characteristics of the gate and its load.
34
Transition Time
•The amount of time that the output of a logic circuit
takes to change from one state to another is called the
transition time.
–t
R
: rise time – time to chage from low to high
–t
F
: fall time – time to chage from high to low
35
Transition Time
•The rise and fall times of a CMOS output depend
mainly on
–“on” transistor resistance
–capacitive load
•Capacitive load = Stray capacitance = AC load
–Output circuits: A gate’s output transistors, internal wiring,
packaging
–The wiring that connects an output to other inputs
–Input circuits: A gate’s input transistors, internal wiring,
packaging
36
Propagation Delay
•The propagation delay is the amount of time that it takes for a
change in the input signal to produce a change in the output signal.
–t
PHL
: high-to-low propogation time
–t
PLH
: low-to-high propogation time
–t
PD
: propogation delay; t
PD
= max (t
PHL
, t
PLH
)
•t
PD
determines the gate speed
37
Power Consumption
•Static power consumption: Power consumption when the
circuit’s output is not changing
–Very low static power consumption for CMOS circuits
•Attractive for low-power applications
•Power consumption due to the leakage currents
•Dynamic power consumption: Power consumption when
the circuit’s output is in transition
P
D
= (C
PD
+ C
L
) x (V
CC
)
2
x f
–P
T
: Dynamic power consumption
–V
CC
: Power-supply voltage
–f: Transition frequency of the output signal
–C
PD
: Power-dissipation capacitance – Specified by the device
manufacturer and around 20-24 pF
–C
L
: Load capacitance
CMOS Logic Family
•4000 series
–First commercially successful CMOS family
–Fairly slow and not easy to interface to TTL
•CMOS device part number: 74FAMnn or 54FAMnn
–HC/HCT: High speed CMOS/ High speed CMOS, TTL
compatible
–FCT/FCT-T: Fast CMOS/ Fast CMOS, TTL compatible
–VHC/VHCT: Very high speed CMOS/ Very high speed CMOS,
TTL compatible
CMOS-TTL Interface
•DC noise margin
–CMOS outputs driving TTL inputs: Ok
–TTL outputs driving CMOS inputs: CMOS device must be HCT,
VHCT or FCT
•Fan-out
–TTL outputs driving CMOS inputs: Ok
–CMOS outputs driving TTL inputs: Limited
•Capacitive loading
–Increasing delay and power consumption
–All CMOS families have similar dynamic power consumption
–TTL outputs have lower dynamic power consumption