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Tutorial: ITI1100

Dewan Tanvir AhmedSITE, UofO

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General Decoder Diagram

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

Decoders

Demo

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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

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

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• Expansion– two 3-to-8 decoder: a 4-to-16 deocder– a 5-to-32 decoder?

Decoder (cont..)

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– 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)

Decoder (cont..)

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Lab-3Something like this:

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BCD to 7-Segment DisplayDesign Requirements

a

b

c

d

e

f gBCD to 7SegmentDecoder

a

b

c

d

e

f

g

X3

X2

X1

X0

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

to 9

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Possible numbers and their representation on 7 segment display

a

b

c

d

e

f b

c

a

b

d

e

g

a

b

c

d

g b

c

f g

a

c

d

f g

a

c

d

e

f g

a

b

c

a

b

c

d

e

f g

a

b

c

f g

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Truth Table

X3 X2 X1 X0 a b c d e f g0 0 0 0 1 1 1 1 1 1 00 0 0 1 0 1 1 0 0 0 00 0 1 0 1 1 0 1 1 0 10 0 1 1 1 1 1 1 0 0 10 1 0 0 0 1 1 0 0 1 10 1 0 1 1 0 1 1 0 1 10 1 1 0 1 0 1 1 1 1 10 1 1 1 1 1 1 0 0 0 01 0 0 0 1 1 1 1 1 1 11 0 0 1 1 1 1 0 0 1 11 0 1 0 x x x x x x x1 0 1 1 x x x x x x x1 1 0 0 x x x x x x x1 1 0 1 x x x x x x x1 1 1 0 x x x x x x x1 1 1 1 x x x x x x x

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Signal b implementation

X1X0

00 01 11 10X3X2

00 1  1  1   1 

01 1 0 1    0 

11 X     X X X

10  1   1  X  X  

b = f(X3, X2, X1, X0) =

X1’X0’

+ X1X0

+ X2’

X3

X2

X1

X0

b

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Signal c implementation

X1X0

00 01 11 10X3X2

00 1  1  1   0 

01 1 1 1    1 

11 X     X X X

10  1   1  X  X  

c = f(X3, X2, X1, X0) =

X1’+

+ X0

+ X2

X3

X2

X1

X0 c

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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

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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

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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

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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

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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

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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.

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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

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Multiplexers (Data Selectors)

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

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Multiplexers Two-input multiplexer

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Multiplexers Four-input multiplexer

Four-input multiplexer - using sum of products logic

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Multiplexers Eight-input multiplexer: The 74151

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Multiplexers Eight-input multiplexer

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Multiplexers (cont..)

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Boolean function implementation– MUX: a decoder + an OR gate– 2

n-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

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– Example: F(A,B,C)=S(1,3,5,6)

Multiplexers (cont..)

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• 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

Multiplexers (cont..)

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

Multiplexers (cont..)

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Exercise

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

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Lab: Multiplexers

Four-input multiplexer - using sum of products logic

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Thank You!