Dr. Wissam Hasan Mahdi Alagele

1 / 38

# Dr. Wissam Hasan Mahdi Alagele - PowerPoint PPT Presentation

وزارة التعليم العالي والبحث العلمي جامعة الكوفة - كلية التربية – قسم علوم الحاسوب. Digital Logic Design I I I. Chapter 3 Decoder and Encoder . Dr. Wissam Hasan Mahdi Alagele. e-mail:wisam.alageeli@uokufa.edu.iq. http :// edu-clg.kufauniv.com/staff/Mr.Wesam. Decoder definition.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Dr. Wissam Hasan Mahdi Alagele' - doli

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

جامعة الكوفة - كلية التربية – قسم علوم الحاسوب

Digital Logic Design III

Chapter 3

Decoder and Encoder

Dr. WissamHasan Mahdi Alagele

e-mail:wisam.alageeli@uokufa.edu.iq

http://edu-clg.kufauniv.com/staff/Mr.Wesam

Decoder definition
• Decoding is the conversion of an n-bit input code to an m-bit output code with n ≤ m ≤ 2n, such that each valid code work produces a unique output code.
• Decoding is performed by a logic circuit called a decoder.
Black box with n input lines and 2n output lines

Only one output is a 1 for any given input

Binary Decoder

Binary

Decoder

n

inputs

2n outputs

A decoder has

N inputs

2N outputs

A decoder selects one of 2N outputs by decoding the binary value on the N inputs.

The decoder generates all of the minterms of the N input variables.

Exactly one output will be active for each combination of the inputs.

Decoders

What does “active” mean?

BinaryDecoder

x1

x0

Decoders

Only onelamp will turn on

• Extract “Information” from the code
• Binary Decoder
• Example: 2-bit Binary Number

0

1

2

3

1

0

0

0

0

0

n-to-m-line decoders
• Circuit has n inputs and m outputs and m ≤ 2n
• This a 1-to-2 Line decoder – exactly one of the output lines will be active.

BinaryDecoder

y3

y2

y1

y0

I1

I0

Decoders

A decoder when n=2 and m=4

A 2-to-4 line decoder

Note that only one output is ever active

BinaryDecoder

Y7

Y6

Y5

Y4 Y3

Y2

Y1

Y0

I2

I1

I0

Decoders
• 3-to-8 Line Decoder
Enable is a common input to logic functions

See it in memories and today’s logic blocks

Enable

BinaryDecoder

Y3

Y2

Y1

Y0

I1

I0

E

Decoders
• “Enable” Control

BinaryDecoder

Y7

Y6

Y5

Y4

Y3

Y2

Y1

Y0

Y3

Y2

Y1

Y0

I0

I1

E

BinaryDecoder

Y3

Y2

Y1

Y0

I0

I1

E

Decoders

I2 I1 I0

• Expansion

BinaryDecoder

BinaryDecoder

Y3

Y2

Y1

Y0

Y3

Y2

Y1

Y0

I1

I0

I1

I0

Decoders
• Active-High / Active-Low

BinaryDecoder

Y7

Y6

Y5

Y4 Y3

Y2

Y1

Y0

x

y

z

I2

I1

I0

S C

Implementation Using Decoders
• Each output is a minterm
• All minterms are produced
• Sum the required minterms

S(x, y, z) = ∑(1, 2, 4, 7)

C(x, y, z) = ∑(3, 5, 6, 7)

BinaryDecoder

BinaryDecoder

Y7

Y6

Y5

Y4 Y3

Y2

Y1

Y0

Y7

Y6

Y5

Y4

Y3

Y2

Y1

Y0

x

y

z

x

y

z

I2

I1

I0

I2

I1

I0

S C

S C

Implementation Using Decoders
An encoder has

2N inputs

N outputs

An encoder outputs the binary value of the selected (or active) input.

An encoder performs the inverse operation of a decoder.

Issues

What if more than one input is active?

What if no inputs are active?

Encoders

x1

x2

x3

1

BinaryEncoder

y1

y0

2

3

Encoders

Only oneswitch should be activated at a time

• Put “Information” into code
• Binary Encoder
• Example: 4-to-2 Binary Encoder

BinaryEncoder

I7

I6

I5

I4 I3

I2

I1

I0

Y2

Y1

Y0

Encoders
• Octal-to-Binary Encoder (8-to-3)

0

2

3

4

5

6

7

1

Encoder / Decoder Pairs

BinaryEncoder

BinaryDecoder

Y7

Y6

Y5

Y4 Y3

Y2

Y1

Y0

I7

I6

I5

I4 I3

I2

I1

I0

7

6

5

Y2

Y1

Y0

I2

I1

I0

4

3

2

1

0

MUX

I0

I1

I2

I3

Y

S1 S0

Multiplexers

MUX

I0

I1

Y

S

MUX

I0

I1

I2

I3

Y

S1 S0

Multiplexers
• 2-to-1 MUX
• 4-to-1 MUX

MUX

I0

I1

MUX

Y

A3

A2

A1

A0

S

MUX

I0

I1

Y3

Y2

Y1

Y0

Y

S

MUX

B3

B2

B1

B0

I0

I1

Y

S

MUX

I0

I1

S E

Y

S

Multiplexers

x3

x2

x1

x0

y3

y2

y1

y0

S

MUX

A3

A2

A1

A0

Y3

Y2

Y1

Y0

B3

B2

B1

B0

S E

Multiplexers

Extra Buffers

MUX

I0

I1

I2

I3

Y

S1 S0

Implementation Using Multiplexers
• ExampleF(x, y) = ∑(0, 1, 3)

1

1

0

1

F

x y

MUX

I0

I1

I2

I3 I4

I5

I6

I7

Y

S2 S1 S0

Implementation Using Multiplexers
• ExampleF(x, y, z) = ∑(1, 2, 6, 7)

0

1

1

0

0

0

1

1

F

x y z

MUX

I0

I1

I2

I3

Y

S1 S0

Implementation Using Multiplexers
• ExampleF(x, y, z) = ∑(1, 2, 6, 7)

z

F = z

F

z

0

F = z

1

F = 0

x y

F = 1

MUX

I0

I1

I2

I3 I4

I5

I6

I7

Y

S2 S1 S0

Implementation Using Multiplexers
• ExampleF(A, B, C, D) = ∑(1, 3, 4, 11, 12, 13, 14, 15)

D

F = D

D

F = D

D

0

F = D

F

0

F = 0

D

F = 0

1

1

F = D

F = 1

F = 1

A B C

I0

I1

I2

I3

I4

I5

I6

I7

MUX

I0

I1

Y

Y

S

MUX

MUX

I0

I1

I2

I3

I0

I1

I2

I3

Y

Y

S1 S0

S1 S0

S2 S1 S0

Multiplexer Expansion
• 8-to-1 MUX using Dual 4-to-1 MUX

1

0 0

DeMUX

Y3

Y2

Y1

Y0

I

S1 S0

DeMultiplexers

2

4

5

6

7

1

0

3

Multiplexer / DeMultiplexer Pairs

MUX

DeMUX

Y7

Y6

Y5

Y4 Y3

Y2

Y1

Y0

I7

I6

I5

I4 I3

I2

I1

I0

7

6

5

4

Y

I

3

2

1

0

S2 S1 S0

S2 S1 S0

Synchronize

x2x1x0

y2 y1 y0

BinaryDecoder

Y3

Y2

Y1

Y0

I1

I0

E

DeMUX

Y3

Y2

Y1

Y0

I

S1 S0

DeMultiplexers / Decoders

A

Y

C

Three-State Gates
• Tri-State Buffer
• Tri-State Inverter

A

Y

C

A

C

B

Three-State Gates

A

Y

C

B

Not Allowed

D

Aif C= 1

Bif C= 0

Y=

Three-State Gates

I3

I2

Y

I1

I0

BinaryDecoder

Y3

Y2

Y1

Y0

I1

I0

E

S1

S0

E