Decoding - Intro to Computer Architecture - Lecture Slides, Slides of Computer Architecture and Organization

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What is Decoding?

Topics covered

• Decoding

• Decoding Expansion

• Encoding

• What are the uses of Encoding?

Decoder

• A Decoder is a device that undoes the encoded

information so that the information is retrieved.

• Known as n -to- 2

n

decoder.

• Used to generate the 2

n

minterms of n input

variables.

• A Minterm is a logical expression of n variables

that employs only the complement operator and

the conjunction operator.

Decoder

• From truth table, a circuit for a 2x4 decoder

would be

• Each output is a 2- variable

Minterm(X'Y', X'Y, XY' or XY).

X Y F 0 F 1 F 2 F 3

F 0 = X'Y'

F 1 = X'Y

F 2 = XY'

F 3 = XY

X Y

Another Example for Decoder

• 3 x 8 Decoder Example:

Here, x, y, z are inputs

• F1 through F7 are

Outputs.

x y z F 0 F 1 F 2 F 3 F 4 F 5 F 6 F 7 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 1

n to 2 n

decoder

output lines

Circuit Diagrams on Decoding.

• This is an example

for the circuit diagram

Decoding.

x y z F 0 F 1 F 2 F 3 F 4 F 5 F 6 F 7 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 1

What is Encoding?

• It is just an inverse of Decoding process.

• An encoder has 2 n^ (or less) input lines and n output lines.

The output lines generate the binary code for the

2 n^ input variables.

Encoding’s Truth Table (8 x 3)

2 n^ :^ :

2 n

to n

encoder

n

output lines