meljun cortes it subjects logic gates
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Logic Gates
Logic Design and Switching
* Property of STI
Page 1 of 26
used to process information in computers
operate on the binary variables that are
symbolically represented by the values 0 and 1
(LOW and HIGH logic)
deals with binary variables and logic operations
applied on these variables
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Logic Gates
Logic Design and Switching
* Property of STI
Page 3 of 26
Two Unary Operators:
buffer
NOT
the symbol “ ” can be used interchangeably with
the symbol “ ’ ”
A = A’ = C
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Logic Gates
Logic Design and Switching
* Property of STI
Page 2 of 26
a special kind of electronic device which can be
used for many important functions
in computers, it is used to serve as a switch,
either ON or OFF
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Logic Gates
Logic Design and Switching
* Property of STI
Page 4 of 26
Logic diagram
composed of logic gates which are the visual
representation of the operators as well as some
of their combinations
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Logic Gates
Logic Design and Switching
* Property of STI
Page 5 of 26
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Logic Gates
Logic Design and Switching
* Property of STI
Page 7 of 26
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Logic Gates
Logic Design and Switching
* Property of STI
Page 6 of 26
TTL Transistor-Transistor Logic
ECL. Emitter-Coupled Logic
MOS Metal-Oxide Semiconductor
CMOS Complementary MOS
BiCMOS Bipolar CMOS
I2L Integrated-Injection Logic
GaAS Gallium Arsenide
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Logic Gates
Logic Design and Switching
* Property of STI
Page 8 of 26
has a high output only when all its inputs are
high
F = A • B or F = AB
Truth table:
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Logic Gates
Logic Design and Switching
* Property of STI
Page 9 of 26
The equivalent to the AND gate using switches
with (a) two inputs and (b) N inputs with N = 4.
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Logic Gates
Logic Design and Switching
* Property of STI
Page 11 of 26
Truth table:
XYZ = X(YZ) = (XY)Z is equivalent to
A • B • C = F
Cascade
to connect the output of one gate to one of the
inputs of another making a chain of gates and
effectively creating a product of products
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Logic Gates
Logic Design and Switching
* Property of STI
Page 10 of 26
Consider the Boolean expression
A • B • C = F
where the inputs A, B, and C can have any
binary value. Implement the expression using a
three-input AND gate. Get all possible input
combinations and their corresponding values for
the output F.
Solution:
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Logic Gates
Logic Design and Switching
* Property of STI
Page 12 of 26
Consider the Boolean expression
A • B • C • D • E = F
where we need to implement a digital circuit
using only binary input AND gates. Since
several combinations exist for solving the
problem, consider at least two solutions using a
minimum amount of gates.
Solution:
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Logic Gates
Logic Design and Switching
* Property of STI
Page 13 of 26
output voltage is high if any or all of the input
voltages are high
algebraically represented by a “+” symbol
can be thought of as having switches in parallel,
with each switch corresponding to an input node
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Logic Gates
Logic Design and Switching
* Property of STI
Page 15 of 26
Implement the Boolean expression of Example
3 using only binary gates with the following
configurations:
a) using two OR gates in cascade
b) using a two-level hierarchical approach
Solution:
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Logic Gates
Logic Design and Switching
* Property of STI
Page 14 of 26
Similar to the case of Example 2, provide the
necessary OR gate implementation for the
Boolean expression
A + B + C = F
What will the result be if the inputs are:
1) A = logic 0; B = logic 0; C = logic 0
2) A = logic 1; B = logic 1; C = logic 1
Solution:
1) A+ B+ C = 0 + 0 + 0 = 0
2) A+ B+ C = 1 + 1 + 1 = 1
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Logic Gates
Logic Design and Switching
* Property of STI
Page 16 of 26
Truth Table for the Three-Input OR Gate
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Logic Gates
Logic Design and Switching
* Property of STI
Page 17 of 26
a gate with only one input signal and only one
output signal
the output state is always the opposite of the
input state
Ao = A’I
Truth table:
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Logic Gates
Logic Design and Switching
* Property of STI
Page 19 of 26
an abbreviation for NOT AND
can also be represented by an AND gate with a
bubble at the output
all input signals must be high to produce a low
output
F = A’B’
Truth Table
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Logic Gates
Logic Design and Switching
* Property of STI
Page 18 of 26
represented either by a “ ’ “ or “ “ symbol
the sole purpose is to invert (or negate) the fed
to it
The symbols for (a) NOT and (b) buffer
Two Types of Pushbutton Switches
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Logic Gates
Logic Design and Switching
* Property of STI
Page 20 of 26
an abbreviation for NOT OR
can be replaced by an OR gate with a bubble at
the output
all inputs must be low to produce a high
output
F = (A + B)’
Truth Table
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Logic Gates
Logic Design and Switching
* Property of STI
Page 21 of 26
The (a) NAND and (b) NOR used as inverters
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Logic Gates
Logic Design and Switching
* Property of STI
Page 23 of 26
XOR Truth Table
XNOR
is simply the XOR followed by an inverter
its operator is usually written as “ “
XNOR Truth Table
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Logic Gates
Logic Design and Switching
* Property of STI
Page 22 of 26
Exclusive-OR operator
symbolically represented by “ ”
similar in output to an OR gate except that the
XOR gate produces a 0 output when both
inputs are 1
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Logic Gates
Logic Design and Switching
* Property of STI
Page 24 of 26
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Logic Gates
Logic Design and Switching
* Property of STI
Page 25 of 26
Truth Table for Three-Input XOR
odd function
the output of the 3-input XOR is 1 if only one
input is equal to 1 or if all the three inputs are
equal to 1 (or when the total number of 1’s is
odd)
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Logic Gates
Logic Design and Switching
* Property of STI
Page 26 of 26
Truth Table for Three-Input XNOR
even function
simply the opposite of the XOR function
when all inputs are 0 or for even occurrences
of a 1 as an input, the output is 1
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