Encoders, Decoders,Multiplexers and Demultiplexers [Compatibility Mode]

Encoders,DecoderDemultiDemulti

Shr

rs,Multiplexers and iplexersiplexers

Prepared By:

Shruti Khatri

[email protected]

ObjecObjec

• Decoders• Encoders• Encoders• Multiplexers• DeMultiplexers

ctivesctives

Multiplexers

44

MultipMultip

A multiplexer has− N control inputsp− 2N data inputs

1 output− 1 outputA multiplexer routes (odata input to the outpudata input to the outpu

− The value of the th d t i t ththe data input tha

lexerslexers

or connects) the selected utut.control inputs determines t i l t d

5

at is selected.

5

MultipMultip

Z = A′ IData

inputs Z A .IControl

input

lexerslexers

I0 + A I1

6

I0 + A.I1

6

MultipMultip

MSB L

Z = A′.B'.I0 + A'.B.I

lexerslexers

A B F

0 0 I0

0 1 I1

1 0 I2

1 1 I1 1 I3

LSB

7

I1 + A.B'.I2 + A.B.I3

7

MultipMultip

MSB LS

Z = A′.B'.C'.I0 + A'.B'.C.IA.B'.C'.I0 + A.B'.C.I1

lexerslexersA B C FA B C F

0 0 0 I0

0 0 1 I1

0 1 0 I2

0 1 1 I3

1 0 0 I4

1 0 1 I5

1 1 0 I6

1 1 1 I7

SB

1 1 1 I7

8

I1 + A'.B.C'.I2 + A'.B.C.I3 + + A'.B.C'.I2 + A.B.C.I3

8

Demultiiplexers

99

DemultiDemultiA demultiplexer hasde u t p e e as

− N control inputs− 1 data input− 1 data input− 2N outputs

A demultiplexer routes (oA demultiplexer routes (othe selected output.

The value of the co− The value of the cothat is selected.

A demultiplexer performsA demultiplexer performsmultiplexer.

iplexersiplexers

or connects) the data input toor connects) the data input to

ntrol inputs determines the outputntrol inputs determines the output

s the opposite function of a

10

s the opposite function of a

10

DemultiDemultiO t WOut0

InI

WXY

Out1Out2

S1 S0

ZOut3

A B W

A B

A B W

0 0 I

0 1 0

1 0 0

1 1 0

iplexersiplexers

W A' B' IW = A'.B'.I

X = A.B'.I

Y = A'.B.I

Z = A.B.I

X Y ZX Y Z

0 0 0

I 0 0

11

0 I 0

0 0 I

11

Decooders

1212

DecoDeco

n-to-2n.n inputs

n to 2

Decode

• Information is represented • Decoding - the conversion

m-bit output code with n <=valid code word produces ap

• Circuits that perform decod• A decoder is a minterm geA decoder is a minterm ge

oderoder

n...

2n outputser

by binary codesn of an n-bit input code to an = m <= 2n such that each a unique output codeq pding are called decodersneratornerator

DecoDecoA decoder has

− N inputs− 2N outputs2 outputs

A decoder selects onedecoding the binary vadecoding the binary vaThe decoder generateth N i t i blthe N input variables.

− Exactly one outpcombination of th

odersoders

e of 2N outputs by alue on the N inputsalue on the N inputs.es all of the minterms of

put will be active for each

14

he inputs.What does “active” mean?

14

DecoDeco

B I0

Out0Out1O tI1A Out2Out3

msb

A B W

Active-h

A B W

0 0 1

0 1 0

1 0 0

1 1 0

odersoders

W A' B'WXY

W = A'.B'

X = A.B'YZ

Y = A'.B

Z = A.B

X Y Z

high outputs

X Y Z

0 0 0

1 0 0

15

0 1 0

0 0 1

15

DecoDeco

B I0

Out0Out1O t

msb

I1A Out2Out3

A B W

Active-l

A B W

0 0 0

0 1 1

1 0 1

1 1 1

odersoders

W (A' B')'W = (A'.B')'

X = (A.B')'WXY Y = (A'.B)'

Z = (A.B)'

YZ

X Y Z

ow outputs

X Y Z

1 1 1

0 1 1

16

1 0 1

1 1 0

16

DecoDecomsb

odersoders

1717

Decoder wDecoder w

high-levelenable

B I0

I1Aenable

Enable

I1A

En

En A B

1 0 01 0 0

1 0 1

1 1 0enabled

1 1 1

0 x xdisabled

with Enablewith Enable

WXY

Out0Out1O t Y

ZOut2Out3

W X Y Z

1 0 0 01 0 0 0

0 1 0 0

0 0 1 0

18

0 0 0 1

0 0 0 0

18

Decoder wDecoder w

B I0

I1Alow-levelenable

Enable

I1A

En

En A B

0 0 00 0 0

0 0 1

0 1 0enabled

0 1 1

1 x xdisabled

with Enablewith Enable

WXY

Out0Out1O t Y

ZOut2Out3

W X Y Z

1 0 0 01 0 0 0

0 1 0 0

0 0 1 0

19

0 0 0 1

0 0 0 0

19

Decoder-BasedCircuits (E

X Y Z C S

S = ∑m (1,2,4,7

C = ∑m (3,5,6,X Y Z C S0 0 0 0 00 0 1 0 1

3 inputs and 8 3-to-8 decoder

0 0 00 1 0 0 10 1 1 1 01 0 0 0 11 0 1 1 01 1 0 1 0

Ah d Al lh

1 1 0 1 01 1 1 1 1

Ahmad Almulhe

d Combinational Example)7)

7)

possible mintermscan be used for implementing this circuit

KFUPM 2009em, KFUPM 2009

3 to 8 D3-to-8 D

3-to-8

D0D1D2D3D

A0ADecoder D4

D5D6D7

A1A2

Ah d Al lhAhmad Almulhe

DecoderDecoder

KFUPM 2009em, KFUPM 2009

Encooders

2222

EncoEnco

.

.2n inputs

2n-to-n

Encoder

• Encoding - the opposite of d

.

.Encoder

Encoding the opposite of dm-bit input code to a n-bit outhat each valid code word pro

• Circuits that perform encodin• Circuits that perform encodin• An encoder has 2n (or fewer)

which generate the binary covaluesvalues

• Typically, an encoder converone bit that is 1 to a binary co

iti i hi h th 1position in which the 1 appea

oderoder

. n outputsr

decoding - the conversion of an

r

decoding the conversion of an tput code with n ≤ m ≤ 2n such oduces a unique output code

ng are called encodersng are called encoders) input lines and n output lines ode corresponding to the input

rts a code containing exactly ode corresponding to the ars.

8 to 3 Encode8-to-3 Encode

D7 D6

8-to-3

D0D1D2D3D

A0A

D7 D6

0 00 0

EncoderD4D5D6D7

A1A2 0 0

0 00 00 00 10 11 0

er (truth table)er (truth table)

inputs outputs

6 D5 D4 D3 D2 D1 D0 A2 A1 A06 D5 D4 D3 D2 D1 D0 A2 A1 A0

0 0 0 0 0 1 0 0 00 0 0 0 1 0 0 0 10 0 0 1 0 0 0 1 00 0 1 0 0 0 0 1 10 1 0 0 0 0 1 0 01 0 0 0 0 0 1 0 10 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 1

8 to 3 Encode8-to-3 Encode

D7 D6

8-to-3

D0D1D2D3D

A0A

10000

00

D7 D6

0 00 0

EncoderD4D5D6D7

A1A2

0000

00 0 0

0 00 00 00 10 11 0

er (truth table)er (truth table)

inputs outputs

6 D5 D4 D3 D2 D1 D0 A2 A1 A06 D5 D4 D3 D2 D1 D0 A2 A1 A0

0 0 0 0 0 1 0 0 00 0 0 0 1 0 0 0 10 0 0 1 0 0 0 1 00 0 1 0 0 0 0 1 10 1 0 0 0 0 1 0 01 0 0 0 0 0 1 0 10 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 1

8 to 3 Encode8-to-3 Encode

D7 D6

8-to-3

D0D1D2D3D

A0A

01000

10

D7 D6

0 00 0

EncoderD4D5D6D7

A1A2

0000

00 0 0

0 00 00 00 10 11 0

er (truth table)er (truth table)

inputs outputs

6 D5 D4 D3 D2 D1 D0 A2 A1 A06 D5 D4 D3 D2 D1 D0 A2 A1 A0

0 0 0 0 0 1 0 0 00 0 0 0 1 0 0 0 10 0 0 1 0 0 0 1 00 0 1 0 0 0 0 1 10 1 0 0 0 0 1 0 01 0 0 0 0 0 1 0 10 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 1

8 to 3 Encode8-to-3 Encode

D7 D6

8-to-3

D0D1D2D3D

A0A

00000

10

D7 D6

0 00 0

EncoderD4D5D6D7

A1A2

0100

01 0 0

0 00 00 00 10 11 0

er (truth table)er (truth table)

inputs outputs

6 D5 D4 D3 D2 D1 D0 A2 A1 A06 D5 D4 D3 D2 D1 D0 A2 A1 A0

0 0 0 0 0 1 0 0 00 0 0 0 1 0 0 0 10 0 0 1 0 0 0 1 00 0 1 0 0 0 0 1 10 1 0 0 0 0 1 0 01 0 0 0 0 0 1 0 10 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 1

8 to 3 Encode8-to-3 Encode

D7 D6

8-to-3

D0D1D2D3D

A0A

00000

11

D7 D6

0 00 0

EncoderD4D5D6D7

A1A2

0001

11 0 0

0 00 00 00 10 11 0

er (truth table)er (truth table)

inputs outputs

6 D5 D4 D3 D2 D1 D0 A2 A1 A06 D5 D4 D3 D2 D1 D0 A2 A1 A0

0 0 0 0 0 1 0 0 00 0 0 0 1 0 0 0 10 0 0 1 0 0 0 1 00 0 1 0 0 0 0 1 10 1 0 0 0 0 1 0 01 0 0 0 0 0 1 0 10 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 1

8 to 3 Encode8-to-3 Encode

D7 D6

8-to-3

D0D1D2D3D

A0A

D7 D6

0 00 0

EncoderD4D5D6D7

A1A2 0 0

0 00 00 00 1

Output equations:0 11 0

Note:

A0 = ?A1 = ?A2 = ?

Note:

er (equations)er (equations)

inputs outputs

6 D5 D4 D3 D2 D1 D0 A2 A1 A06 D5 D4 D3 D2 D1 D0 A2 A1 A0

0 0 0 0 0 1 0 0 00 0 0 0 1 0 0 0 10 0 0 1 0 0 0 1 00 0 1 0 0 0 0 1 10 1 0 0 0 0 1 0 01 0 0 0 0 0 1 0 10 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 1

This truth table is not complete! Why?This truth table is not complete! Why?

8 to 3 Encode8-to-3 Encode

D7 D6

8-to-3

D0D1D2D3D

A0A

D7 D6

0 00 0

EncoderD4D5D6D7

A1A2 0 0

0 00 00 00 1

Output equations:0 11 0A0 = D1 + D3 + D5 + D7

A1 = ?A2 = ?

er (equations)er (equations)

inputs outputs

6 D5 D4 D3 D2 D1 D0 A2 A1 A06 D5 D4 D3 D2 D1 D0 A2 A1 A0

0 0 0 0 0 1 0 0 00 0 0 0 1 0 0 0 10 0 0 1 0 0 0 1 00 0 1 0 0 0 0 1 10 1 0 0 0 0 1 0 01 0 0 0 0 0 1 0 10 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 1

8 to 3 Encode8-to-3 Encode

D7 D6

8-to-3

D0D1D2D3D

A0A

D7 D6

0 00 0

EncoderD4D5D6D7

A1A2 0 0

0 00 00 00 1

Output equations:0 11 0A0 = D1 + D3 + D5 + D7

A1 = D2 + D3 + D6 + D7A2 = ?

er (equations)er (equations)

inputs outputs

6 D5 D4 D3 D2 D1 D0 A2 A1 A06 D5 D4 D3 D2 D1 D0 A2 A1 A0

0 0 0 0 0 1 0 0 00 0 0 0 1 0 0 0 10 0 0 1 0 0 0 1 00 0 1 0 0 0 0 1 10 1 0 0 0 0 1 0 01 0 0 0 0 0 1 0 10 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 1

8 to 3 Encode8-to-3 Encode

D7 D6

8-to-3

D0D1D2D3D

A0A

D7 D6

0 00 0

EncoderD4D5D6D7

A1A2 0 0

0 00 00 00 1

Output equations:0 11 0A0 = D1 + D3 + D5 + D7

A1 = D2 + D3 + D6 + D7A2 = D4 + D5 + D6 + D7

er (equations)er (equations)

inputs outputs

6 D5 D4 D3 D2 D1 D0 A2 A1 A06 D5 D4 D3 D2 D1 D0 A2 A1 A0

0 0 0 0 0 1 0 0 00 0 0 0 1 0 0 0 10 0 0 1 0 0 0 1 00 0 1 0 0 0 0 1 10 1 0 0 0 0 1 0 01 0 0 0 0 0 1 0 10 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 1

8 to 3 Enco8-to-3 Enco

8-to-3

D0D1D2D3D

A0AEncoderD4

D5D6D7

A1A2

Output equations:

A0 = D1 + D3 + D5 + D7A1 = D2 + D3 + D6 + D7A2 = D4 + D5 + D6 + D7

oder (circuit)oder (circuit)

D

A0

D1D3D5D7

A1

D2D3D6D7

A2D4D5D6D7

8 to 3 Encode8-to-3 Encode

D7 D6

Two Limitations:D7 D6

0 00 0

1. Two or more inputs = 1• Example: D3 = D6 = 1• A2A1A0 = 111

0 00 0

2. All inputs = 0• Same as D0 =1

Output equations:

0 00 00 1

A0 = D1 + D3 + D5 + D7A1 = D2 + D3 + D6 + D7A2 = D4 + D5 + D6 + D7

0 11 0

er (limitations)er (limitations)

inputs outputs

6 D5 D4 D3 D2 D1 D0 A2 A1 A06 D5 D4 D3 D2 D1 D0 A2 A1 A0

0 0 0 0 0 1 0 0 00 0 0 0 1 0 0 0 10 0 0 1 0 0 0 1 00 0 1 0 0 0 0 1 10 1 0 0 0 0 1 0 01 0 0 0 0 0 1 0 10 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 1