Tutorial: ITI1100

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```					Tutorial: ITI1100

Dewan Tanvir Ahmed
SITE, UofO

1
Decoders
Decoder - logic circuit that activates an output that corresponds
to a binary number on the input (set of inputs).

General Decoder Diagram

Demo
2
Decoder
•   A n-to-m decoder
n
– a binary code of n bits = 2 distinct information
n
– n input variables; up to 2 output lines
– only one output can be active (high) at any time

3
Three-line-to 8-line (or 1-of-8) decoder

4
Decoder (cont..)
•   Expansion
– two 3-to-8 decoder: a 4-to-16 deocder
– a 5-to-32 decoder?

5
Decoder (cont..)
– each output = a minterm
– use a decoder and an external OR gate to implement any Boolean function of n input
variables
• S(x,y,x)=S(1,2,4,7)
• C(x,y,z)= S(3,5,6,7)

6
Lab-3
Something like this:

7
BCD to 7-Segment Display
Design Requirements

X3
a
a

X2           BCD to 7              b        f     g     b
c

X1           Segment               d
e           c
e

X0           Decoder               f

g              d

Design the logic circuitry that will drive a seven segment LED
display and will be able to represent numbers from 0 to 9

8
Possible numbers and their representation on
7 segment display
a                           a               a                                 a

f         b           b           g       b       g   b f       g       b       f   g

e             c       c       e                       c                 c               c

d                           d               d                                 d

a           a                   a                 a

f       g                   b       f   g   b     f       g       b

e               c           c e             c                     c

d                               d
9
Truth Table
X3   X2   X1   X0     a   b   c   d   e   f   g
0    0    0    0      1   1   1   1   1   1   0
0    0    0    1      0   1   1   0   0   0   0
0    0    1    0      1   1   0   1   1   0   1
0    0    1    1      1   1   1   1   0   0   1
0    1    0    0      0   1   1   0   0   1   1
0    1    0    1      1   0   1   1   0   1   1
0    1    1    0      1   0   1   1   1   1   1
0    1    1    1      1   1   1   0   0   0   0
1    0    0    0      1   1   1   1   1   1   1
1    0    0    1      1   1   1   0   0   1   1
1    0    1    0      x   x   x   x   x   x   x
1    0    1    1      x   x   x   x   x   x   x
1    1    0    0      x   x   x   x   x   x   x
1    1    0    1      x   x   x   x   x   x   x
1    1    1    0      x   x   x   x   x   x   x
1    1    1    1      x   x   x   x   x   x   x

10
Signal b implementation

X1X0
b = f(X3, X2, X1, X0) =
X3X2          00    01   11   10

00    1     1    1    1
X1’X0’
01    1     0    1    0       + X1X0

+ X2’
11    X     X    X    X

10    1     1    X    X

X3

X2

X1                                        b

X0
11
Signal c implementation

X1X0
c = f(X3, X2, X1, X0) =
X3X2          00        01   11   10

00     1         1    1    0
X1’+
01     1         1    1    1       + X0

+ X2
11     X         X    X    X

10     1         1    X    X

X3

X2

X1

X0                       c
12
7 segment display

• All the anode segments are connected together
• Power must be applied externally to the anode connection that is common
to all the segments
• By applying the ground to a particular segment (i.e. a,b,g etc..), the
appropriate segment will light up

13
7 segment common anode

• A resistor should be added in order to limit the current through
LED
• The current to light the active LED is sink by the logic component,
which is preferable
14
7 segment display

•   All the cathode of the LED are connected together
•   The common connection must be grounded and power must be applied to
appropriate segment in order to illuminate that segment
•   The current to light the active LED is generated by the logic component,
which generates the logic 1

15
BCD to 7 Segment Decoder/Drivers

•   Common-anode : requires VCC , LED ON when
Output is LOW.

•   Common-cathode : NO VCC , LED ON when
Output is HIGH.

•   TTL and CMOS devices are normally not used to
drive the common-cathode display directly
because of current (mA) requirement. A buffer
circuit is used between the decoder chips and
common-cathode display

16
7447 TTL IC
•   Real world example of BCD
to 7 segment decoder
•   Outputs of the decoder are
active low and a common
anode 7 segment display is
used

17
Lab: BCD to 7 Segment Decoder/Drivers

(a) BCD-to-7-segment
decoder/driver
driving a common-
anode 7-segment
LED display;

(b) segment patterns
for all possible
input codes.

18
Multiplexers (Data Selectors)
•   A multiplexer (MUX) selects one of multiple input signals and passes it to the
output.
•   The basic two input multiplexer
•   The four input multiplexer
•   The eight input multiplexer

19
Multiplexers (Data Selectors)
•   A multiplexer (MUX)
selects 1 out of N input
data sources and
transmits the selected
data to a single output

20
Multiplexers
Two-input multiplexer

21
Multiplexers
Four-input multiplexer

Four-input multiplexer - using sum of products logic

22
Multiplexers
Eight-input multiplexer: The 74151

23
Multiplexers
Eight-input multiplexer

24
Multiplexers (cont..)

25
Boolean function implementation
– MUX: a decoder + an OR gate
n
– 2 -to-1 MUX can implement any Boolean function of n input variable
– a better solution: implement any Boolean function of n+1 input variable
• n of these variables: the selection lines
• the remaining variable: the inputs

26
Multiplexers (cont..)
– Example: F(A,B,C)=S(1,3,5,6)

27
Multiplexers (cont..)
•   Procedure:
– assign an ordering sequence of the input variable
– the leftmost variable (A) will be used for the input lines
– assign the remaining n-1 variables to the selection lines w.r.t. their corresponding
sequence
– list all the minterms in two rows (A' and A)
– circle all the minterms of the function
– determine the input lines

28
Multiplexers (cont..)
•   An example: F(A,B,C,D)=S(0,1,3,4,8,9,15)

29
Exercise
•   Try to build an inverter using 2-1 MUX
•   Try to build XOR gate using 4-1 MUX

30
Lab: Multiplexers

Four-input multiplexer - using sum of products logic

31
Thank You!

32

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