Transcript DGD

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
– A full-adder
• 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
a
X3
X2
X1
X0
BCD to 7
Segment
Decoder
a
b
f
g
b
c
d
e
e
c
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
f
b
b
e
c
c
a
b
g
g
e
d
f
e
d
f
f
g
c e
g
c
c
d
a
b
c
b
g
d
a
g
b f
c
d
a
a
a
b
c
f
g
b
c
d
9
Truth Table
X3
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
X2
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
X1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
X0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
a
1
0
1
1
0
1
1
1
1
1
x
x
x
x
x
x
b
1
1
1
1
1
0
0
1
1
1
x
x
x
x
x
x
c
1
1
0
1
1
1
1
1
1
1
x
x
x
x
x
x
d
1
0
1
1
0
1
1
0
1
0
x
x
x
x
x
x
e
1
0
1
0
0
0
1
0
1
0
x
x
x
x
x
x
f
1
0
0
0
1
1
1
0
1
1
x
x
x
x
x
x
g
0
0
1
1
1
1
1
0
1
1
x
x
x
x
x
x
10
Signal b implementation
X1X0
00
01
11
10
00
1
1
1
1
01
1
0
1
0
11
X
X
X
X
10
1
1
X
X
X3X2
b = f(X3, X2, X1, X0) =
X1’X0’
+ X1X0
+ X2’
X3
X2
X1
X0
b
11
Signal c implementation
X1X0
00
01
11
10
00
1
1
1
0
01
1
1
1
1
11
X
X
X
X
10
1
1
X
X
X3X2
c = f(X3, X2, X1, X0) =
X1’+
+ X0
+ X2
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 commonanode 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