1. Dewan Tanvir Ahmed SITE, UofO
Tutorial: ITI1100
Dewan Tanvir Ahmed
SITE, UofO

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

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

4. Three-line-to 8-line (or 1-of-8) decoder

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

6. 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)

7. Lab-3
Something like this:

8. BCD to 7-Segment Display Design Requirements
Design the logic circuitry that will drive a seven segment LED display and will be able to represent numbers from 0 to 9
The BCD to 7-segment decoder performs a common function: it converts the binary representation of a decimal digit, 0000 to 1001, to the signals needed to show the digit on a 7 segment display.

9. Possible numbers and their representation on 7 segment display

10. Truth Table

11. Signal b implementation
X1X0 00 01 11 10
X3X2 1  1
 1 
1  
 0 
X  
  X X X 
b = f(X3, X2, X1, X0) =
X1’X0’
+ X1X0
+ X2’

12. Signal c implementation
X1X0 00 01 11 10
X3X2 1  1
 1 
 0 
1  
X  
  X X X 
c = f(X3, X2, X1, X0) =
X1’+
+ X0
+ X2

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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.

19. 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

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

21. Multiplexers Two-input multiplexer

22. Multiplexers Four-input multiplexer
Four-input multiplexer - using sum of products logic

23. Multiplexers Eight-input multiplexer: The 74151

24. Multiplexers Eight-input multiplexer

25. Multiplexers (cont..)

26. Boolean function implementation
MUX: a decoder + an OR gate
2n-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

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

28. 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

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

30. Exercise Try to build an inverter using 2-1 MUX
Try to build XOR gate using 4-1 MUX

31. Lab: Multiplexers
Four-input multiplexer - using sum of products logic

32. Thank You!