chapter 2 logic functions and gates. 2 basic logic functions the three basic logic functions are:...
TRANSCRIPT
Chapter 2
Logic Functions and Gates
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Basic Logic Functions
• The three basic logic functions are:– AND– OR– NOT
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Logic Function Representation
• Logic functions can be represented:–algebraically–using truth tables–using electronic circuits.
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Algebraic Representation
• Uses Boolean algebra.
• Boolean variables have two states (binary).
• Boolean operators include AND, OR, and NOT.
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Truth Table Representation
• Defines the output of a function for every possible combination of inputs.
• A system with n inputs has 2n possible combinations.
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Electronic Circuit Representation
• Uses logic gates to perform Boolean algebraic functions.
• Gates can be represented by schematic symbols.
• Symbols can be either distinctive-shape or rectangular-outline.
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Distinctive Shape Schematic Symbols
• Uses different graphic representations for different logic functions.
• Uses a bubble (a small circle) to indicate a logical inversion.
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Rectangular-Outline Schematic Symbols
• All functions are shown in rectangular form with the logic function indicated by standard notation inside the rectangle.
• The notation specifying the logic function is called the qualifying symbol.
• Inversion is indicated by a 1/2 arrowhead.
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NOT Function
• One input and one output.
• The output is the opposite logic level of the input.
• The output is the complement of the input.
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NOT Function Boolean Representation
• Inversion is indicated by a bar over the signal to be inverted.
A Y
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NOT Function Electronic Circuit
• Called a NOT gate or, more usually, an INVERTER.
• Distinctive-shape symbol is a triangle with inversion bubble.
• Rectangular-shape symbol uses “1” and the inversion 1/2 arrowhead.
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NOT Function Electronic Circuit
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AND Function
• Two or more inputs, one output.
• Output is HIGH only when all of the inputs are HIGH.
• Output is LOW whenever any input is LOW.
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A B Y0 0 0
0 1 01 0 01 1 1
AND Function
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AND Boolean Representation
• AND symbol is “•” or nothing at all.
ABY
B AY
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AND Function Electronic Circuit
• Called an AND gate.
• Distinctive-shape symbol uses AND designation.
• Rectangular-shape symbol use “&” as designator.
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AND Function Electronic Circuit
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AND Function Electronic Circuit
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A B C Y0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 0
1 0 0 0
1 0 1 0
1 1 0 0
1 1 1 1
AND Function Electronic Circuit
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OR Function
• Two or more inputs, one output.
• Output is HIGH whenever one or more input is HIGH.
• Output is LOW only when all of the inputs are LOW.
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OR Function
A B Y
0 0 0
0 1 0
1 0 1
1 1 1
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OR Boolean Representation
• OR symbol is “+”.
• Y = A + B
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OR Function Electronic Circuit
• Called an OR gate.
• Distinctive-shape symbol uses OR designation.
• Rectangular-shape symbol uses “” as designator.
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OR Function Electronic Circuit
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Active Level
• The logic level defined as “ON” for a circuit.
• When a logic HIGH is “ON”, the signal is active-HIGH.
• When a logic LOW is “ON”, the signal is active-LOW.
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NAND Function
• Generated by inverting the output of the AND function.
• Output is HIGH whenever any input is LOW.
• Output is LOW only when all inputs are HIGH.
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NAND Function
A B Y
0 0 1
0 1 1
1 0 1
1 1 0
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NAND Boolean Representation
• Uses AND with an inversion overbar.
BA Y
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NAND Function Electronic Circuit
• Called a NAND gate.
• Uses the AND symbol with inversion on.
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NAND Function Electronic Circuit
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NOR Function
• Generated by inverting the output of the OR function.
• Output is HIGH only when all inputs are LOW.
• Outputs is LOW whenever any input is HIGH.
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A B Y0 0 1
0 1 0
1 0 0
1 1 0
NOR Function
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NOR Boolean Representation
• Uses OR with an inversion overbar.
B A Y
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NOR Function Electronic Circuit
• Called a NOR gate.
• Uses OR symbol with inversion on the output.
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NOR Function Electronic Circuit
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3 Input NOR and NAND FunctionTruth Tables
• 3 Input NAND:
• 3 Input NOR:
CBA Y
C B A Y
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A B C0 0 0 1 10 0 1 1 00 1 0 1 00 1 1 1 01 0 0 1 01 0 1 1 01 1 0 1 01 1 1 0 0
C B A CBA
3 Input NOR and NAND FunctionTruth Tables
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Exclusive OR Gate
• Two inputs, one output.
• Output is HIGH when one, and only one, input is HIGH.
• Output is LOW when both inputs are equal – both HIGH or both LOW.
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Exclusive OR Gate
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A B Y0 0 0
0 1 1
1 0 1
1 1 0
Exclusive OR Gate
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Exclusive NOR Gate
• Two inputs, one output.
• Output is HIGH when both inputs are equal – both HIGH or both LOW.
• Output is LOW when one, and only one, input is HIGH.
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Exclusive NOR Gate
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A B Y0 0 1
0 1 0
1 0 0
1 1 1
Exclusive NOR Gate
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Gate Equivalence – NAND
• A NAND gate can be represented by an AND gate with inverted output.
• A NAND gate can be represented by an OR gate with inverted inputs.
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Gate Equivalence – NAND
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Gate Equivalence – NOR
• A NOR gate can be represented by an OR gate with inverted output.
• A NOR gate can be represented by an AND gate with inverted inputs.
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Gate Equivalence – DeMorgan Forms
• Change an AND function to an OR function and an OR function to an AND function.
• Invert the inputs.
• Invert the outputs.
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DeMorgan’s Theorem - 1
•
•
• Break the line and change the sign
B A BA B A BA
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DeMorgan’s Theorem - 2
• The following are two common errors associated with DeMorgan’s Theorem:
•
• B A BA B A BA
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Active Logic Levels
• Any INPUT or OUTPUT that has a BUBBLE is considered as active LOW.
• Any INPUT or OUTPUT that has no BUBBLE is considered as active HIGH.
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Active Logic Levels - NOR
•
• At least one input HIGH makes the output LOW.
•
• All inputs LOW make the output HIGH.
BA Y
BA Y
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Active Logic Levels - NOR
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Logic Switches
• Provides a logic HIGH or LOW depending on switch position.
• Commonly used types include normally-open pushbutton, normally-closed pushbutton, single-pole single-throw, and single-pole double-throw.
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Logic Switches
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Logic Switches
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Two-Pole Push Button
• Two-pole push button allows for normally HIGH and normally LOW levels from the same switch.
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Two-Pole Push Button
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Light Emitting Diodes (LED’s)
• Used to indicate the status of a digital output.
• Has two terminals the anode and the cathode.
• If the anode is approximately 1.5 V greater than the cathode, current flows and the LED illuminates.
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Light Emitting Diodes (LED’s)
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Light Emitting Diodes (LED’s)
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Light Emitting Diodes
• Used to provide a visual indication of a logic state.
• Can be wired to display active-HIGH or active-LOW.
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Light Emitting Diodes
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Light Emitting Diodes
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Logic Gate Enable
• The input to a gate that allows the output to respond to other inputs.
• A logic LOW for an OR or NOR gate, a logic HIGH for an AND or NAND gate.
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Logic Gate Inhibit
• The input to a gate that forces the output to ignore any other input.
• A logic HIGH for an OR or NOR gate, a logic LOW for an AND or NAND gate.
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Logic Gate Inhibit
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Logic Gate Inhibit
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Logic Gate Inhibit
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Logic Gate Inhibit
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Logic Gate Inhibit
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Logic Gate Inhibit
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Control AND OR NAND NOR XOR XNOR
A = 0 Y = 0 Y = B Y = 1 Y = B
A = 1 Y = B Y = 1 Y = 0 Y = BB Y
B Y
B Y
B Y
Logic Gate Inhibit
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Tristate Buffer
• Three output states, HIGH, LOW and high-impedance.
• Requires a separate input to control which output state is selected.
74
Tristate Buffer
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Tristate Buffer
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Tristate Buffer Utilization
• Used to connect multiple outputs together.
• Used in controlling the operation of buses.
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Tristate Buffer Utilization
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The 74LS244 Octal Tri-State Buffer
• Contains two groups of four non-inverting tri-state buffers.
• Each group is controlled by a separate enable input.
G
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The 74LS244 Octal Tri-State Buffer
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Integrated Circuit Package
• Integrated Circuits (ICs) contain many components in a single package.
• Several packaging options are available.
• One common package is called dual-in-line (DIP).
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Integrated Circuit Package
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Integrated Circuit Technology
• One common form is transistor-transistor logic, called TTL.
• The other common form is Complementary Metal-Oxide Semiconductor, called CMOS.
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Part Number Logic Family74LS00 Low-power Schottky TTL
74ALS00 Advanced low-power Schottky TTL
74F00 FAST TTL
74HC00 High-speed CMOS
74CT00 High-speed CMOS (TTL-compatible inputs)
74LVX00 Low-voltage CMOS
74ABT00 Advanced BiCMOS (TTL/CMOS hybrid)
Integrated Circuit Technology
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Integrated Circuit Designation
• Standard form is 74XXFF, where 74 is the logic family identifier, XX is the logic family member and FF identifies the specific logic function.
• SN74ALS00N
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IC Package Options
• PLCC - plastic lead chip carrier • SOIC - small outline integrated circuit • TSSOP – thin shrink small outline
package• QFP – quad flat pack• DIP – dual inline package• BGA – ball grid array
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IC Package Options
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PLCC 84 Pin Packages• Can be mounted on the surface of a
circuit board or mounted in a socket.
• Pins are equally distributed on four sides.
• Pin 1 placed on the center of one of the rows, as indicated by a dot.
• Pins number counterclockwise from this point.
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PLCC 84 Pin Packages