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7/28/2019 ES ZC261-L5
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BITS PilaniPilani Campus
DIGITAL ELECTRONICS
AND MICROPROCESSORRekha.A
Faculty
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Full Subtractor
Block diagram of full subtractor Truth table of full subtractor
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K-Map for Full Subtractor
1 1
1 1
x
yz
00 01 11 10
0
1
D= xyz + xyz + xyz+ xyz
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K-Map for Borrow of full subtractor
1 1 1
1
x
yz00 01 11 10
0
1
B = xz+xy+yz
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Implementation of full subtractor
B
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Four bit binary Adder-Subtractor
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Comparators
Comparators are designed to compare the magnitude of two binary
numbers and indicate whether one is greater than, less than or
equal to the other.
One bit comparator
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Implementation of one bit comparator
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Two bit comparator
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Truth table of 2 bit comparator
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Decoders
Discrete quantities of information are represented in digital systemsby binary codes
A decoder is a combinational circuit that converts the binaryinformation from n input lines to a maximum of 2n output lines.
A decoder is a device which when activated , selects one of itspossible 2n outputs based on its n bit digit.
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General representation of a decoder
12ESZC261:Digital Electronics and Microprocessor
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2 to 4 Decoder
13ESZC61:Digital Electronics and Microprocessor
Y0
Y1
Y2
Y3
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Dual 2 to 4 line Decoder
14ESZC261:Digital Electronics and Microprocessor
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Implement with a suitable decoder with active low enable input for the
function f(w,x,y,z) = (3,7,9)
15ESZC261:Digital Electronics and Microprocessor
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Implement the function with a suitable decoder
F = (0,1,3,5,6 )
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4 to 16 decoder constructed as 3 to 8 decoder
W X Y Z
0 0 0 0
0 0 0 1
0 0 1 0
0 0 1 1
0 1 0 00 1 0 1
0 1 1 0
0 1 1 1
1 0 0 0
1 0 0 1
1 0 1 01 0 1 1
1 1 0 0
1 1 0 1
1 1 1 0
1 1 1 1
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Implementation of a Full adder with a decoder
S= (1,2,4,7)
C=(3,5,6,7)
19ESZC261:Digital Electronics and Microprocessor
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ENCODERS
Decoders accept an input code and produce a HIGH(or LOW) at
one output line.Decoder identifies, recognise or detects a particular
code
An encoder has a number of input lines , only one of which is
activated at a given time and produces an n-bit output code,
depending on which input is activated.
An Encoder has 2n(or fewer) input lines and n output lines.
The output lines as an aggregate, generate the binary code
corresponding to the input value.
20ESZC261:Digital Electronics and Microprocessor
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A General Block Diagram of an Encoder
21ESZC261:Digital Electronics and Microprocessor
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Truth Table of a 8 to 3 line Encoder( Decimal to BCD)
22ESZC261:Digital Electronics and Microprocessor
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Priority Encoder
A priority encoder is an encoder circuit that includes the priority
function.
When more than one inputs are equal to 1 at the same time, the
input having the highest priority will take precedence.
In addition to the outputs, the circuit has the output designated as V
which is the valid bit.
Valid bit indicator is set to 1 when one or more inputs are equal to 1.
23ESZC261:Digital Electronics and Microprocessor
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Truth Table of 8 to 3 line priority Encoder
24ESZC261:Digital Electronics and Microprocessor
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K Map for the outputs
X2X3 X2X3
1 1 1
1 1 1
1 1 1
1 1 1
1 1
1 1 1
1 1 1
1 1
X0 X1
00
01
11
10
00 01 11 10 00 01 11 10
00
01
11
10
y1 = x2 + x3 y0 = x3+ x1x2
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A multiplexer is a combinational circuit that selects binary information
from one of the many input lines and directs it to a single output line.
The selection of a particular input line is controlled by a set of selectionlines.
2n input lines , n select lines whose bit combinations determine which
input is selected.
26ESZC261:Digital Electronics and Microprocessor
MULTIPLEXER
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Block Diagram of a two to one line multiplexer
When S=0, Io is selected
When S=1, I1 is selected
27ESZC261:Digital Electronics and Microprocessor
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Logic Diagram of a Two-to-One line multiplexer
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Four to one line multiplexer
Function Table
Implementation of 4 to 1 Mux
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16 to 1 MUX configured using 4 to 1 MUX
30ESZC261:Digital Electronics and Microprocessor
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Implement the following function using a 8 to 1 MUX
f(a,b,c) = (0,4,5,6)
31ESZC261:Digital Electronics and Microprocessor
Boolean Function Implementation
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Implement the following Boolean function using 4 to 1 MUX
F(x,y,z) = (1,2,6,7)
32ESZC261:Digital Electronics and Microprocessor