ECE 2372 Modern Digital System Design Section 4.2 Decoders 1.

ECE 2372Modern Digital System Design

Section 4.2

Decoders

1

Decoders• A decoder is a circuit used to “translate” a code

word to another code representation.

2

Decodersn – 2n Decoder: n-input lines (n-bit word input) and 2n output lines. For each possible word, one (and only one) output is asserted to a logical 1, all other lines will remain at logical 0.

x0 y0

x1

xn

y1

y2n 1

n – 2n Decoder

3

DecodersParallel 2-Bit Decoder (with inputs A and B, and outputs m0, m1, m2, and m3) is described by the

truth table: A m0 B m1 2 – 4

Decoder m2 m3

B A m0 m1 m2 m3 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 1 1 0 0 0 1

4

DecodersB A m0 m1 m2 m3 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 1 1 0 0 0 1

m0 = B–

A–

m1 = B–

A

m2 = B A–

m3 = B A

5

Decoders

m0 = B–

A–

m1 = B–

A

m2 = B A–

m3 = B A

m 0 m 0

A B

m 1 m 0

m 2 m 0

m 3 m 0

6

Decoders• Enable Controls provide a

selection to either inhibit (disable) or allow (enable) the decoder output.

m0 = B–

A–

E

m1 = B–

A E

m2 = B A–

E

m3 = B A E

m 0 m 0

A B

m 1 m 0

m 2 m 0

m 3 m 0

E 7

Decoders• An alternative decoder structure is:

A B

m1

m0

m2

m3

8

74139 2-Line-to-4-Line Decoder/Demultiplexer

9


10


11


12


A B

G

Y0 Y1 Y2 Y3

74139

Enable Select Outputs G B A Y0 Y1 Y2 Y3 L L L L H H H L L H H L H H L H L H H L H L H H H H H L H H H H H

13


14


15


16


17


18


A B

G2A

Y0 Y1 Y2 Y3

74138

Y4 Y5 Y6 Y7

G2B G1

C

19


Enable Select Outputs G1 G2A G2B C B A Y0 Y1 Y2 Y3 Y4 Y5 Y6 Y7 H L L L L L L H H H H H H H H L L L L H H L H H H H H H H L L L H L H H L H H H H H H L L L H H H H H L H H H H H L L H L L H H H H L H H H H L L H L H H H H H H L H H H L L H H L H H H H H H L H H L L H H H H H H H H H H L H H H H H H H H H H H H H H H H H H L H H H H H H H H

20


21


22


23


24


A B

G1

Y0 Y1 Y2 Y3

74154

Y4 Y5 Y6 Y7

G2

C D

Y0 Y1 Y2 Y3 Y4 Y5 Y6 Y7

25


En Select Outputs G1

G2

D C B A 0 1 2 3 4 5 6 7 8 9 10

11

12

13

14

15

L L L L L L L H H H H H H H H H H H H H H H L L L L L H H L H H H H H H H H H H H H H H L L L L H L H H L H H H H H H H H H H H H H L L L L H H H H H L H H H H H H H H H H H H L L L H L L H H H H L H H H H H H H H H H H L L L H L H H H H H H L H H H H H H H H H H L L L H H L H H H H H H L H H H H H H H H H L L L H H H H H H H H H H L H H H H H H H H L L H L L L H H H H H H H H L H H H H H H H L L H L L H H H H H H H H H H L H H H H H H L L H L H L H H H H H H H H H H L H H H H H L L H L H H H H H H H H H H H H H L H H H H L L H H L L H H H H H H H H H H H H L H H H L L H H L H H H H H H H H H H H H H H L H H L L H H H L H H H H H H H H H H H H H H L H L L H H H H H H H H H H H H H H H H H H H L H L H H H H H H H H H H H H H H H H L H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H 26

Applications of Decoders • Implementing Logic Functions Using Decoders:• The Decoder selects an output line corresponding

to the minterm represented by the binary value of the input word.

• This can be used to implement any switching function, often with fewer integrated circuits.

27

Applications of Decoders• Consider the (simplified) 3-Line-to-8-Line

Decoder and the switching function:

A m0 B C

Y0 Y1 Y2 Y3 Y4 Y5 Y6 Y7

a b c m2

m3

m4

m5 m6

m7

m1

f (c, b, a) = m1 + m4 + m6

f (c, b, a) = m1 + m4 + m6

f (c, b, a) = m1 m4 m6

f (c, b, a) = m1 m4 m6

28

Applications of Decoders

f (c, b, a) = m1 + m4 + m6 = m1 m4 m6

f (c, b, a)

A B C

Y0 Y1 Y2 Y3 Y4 Y5 Y6 Y7

a b c

m4

m6

m1

29

Applications of Decoders• Consider the (simplified) 3-Line-to-8-Line

Decoder and the switching function:

f (c, b, a) = M2 M5 M7 M0 M1 M2 M3 M4 M5 M6 M7

A B C

Y0 Y1 Y2 Y3 Y4 Y5 Y6 Y7

a b c

30

Applications of Decoders

f (c, b, a) = M2 M5 M7

f (c, b, a)

A B C

Y0 Y1 Y2 Y3 Y4 Y5 Y6 Y7

a b c

31

Applications of Decoders• Recall, the 4-person vote-tallying machine may be

implemented by:

T = m3 + m5 + m6 + m9 + m10 + m12

P = m7 + m11 + m13 + m14 + m15

F = m0 + m1 + m2 + m4 + m8

32

A

B

C

0

1

2

3

4

5

6

7

x4 F

D

x3

x2

x1

8

9

10

11

12

13

14

15

T

P 33

Applications of Decoders• Address Decoding: One of 2n – 1 devices is

selected when the address of that device is broadcast over a common data bus and decoded by the decoder.

A0

Device 0

A1 An

n – 2n Decoder

Data Bus

Device 1

Device 2n 1

34

Applications of Decoders• BCD to Decimal Decoders: The input is a BCD

word (DCBA), the output is one of the output lines (Y0 – Y9). The inputs are related to the outputs by

the truth table (note don’t-cares).

35

D C B A Y0 Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1

36

Applications of Decoders• Display Decoders: LED displays require

decoders to illuminate the appropriate LED for a given code word.

• An LED emits light when it is forward biased and current flows from anode to cathode. Typically a current limiting resistor must be included in series with the LED.

R

V i

+

37

Applications of Decoders• A number of LEDs (as in a display) may be

connected common anode (LEDs illuminate with logical 0 input).

+VCC

a b c d e f g

38

Applications of Decoders• A number of LEDs (as in a display) may be may

be connected common cathode (LEDs illuminate with logical 1 input).

a b c d e f g

39

Applications of Decoders• In a seven-segment display the individual LEDs

are arranged:

a

b

c d

e

f g

40

Applications of Decoders• The numerals 0 – 9 are represented by:

41

Inputs Outputs X3 X2 X1 X0 a b c d e f g 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 1 1 1 1 0 0 1 0 1 0 0 0 1 1 0 0 1 1 0 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 0 1 0 x x x x x x x 1 0 1 1 x x x x x x x 1 1 0 0 x x x x x x x 1 1 0 1 x x x x x x x 1 1 1 0 x x x x x x x 1 1 1 1 x x x x x x x 42

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ECE 2372 Modern Digital System Design Section 4.2 Decoders 1.

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