5.5 Code
Converter
Encoders
and decoders are fundamental components in the vast landscape of communication
and data processing, acting as the crucial bridge between raw information and
its transmittable or interpretable form. At their core, these paired mechanisms
facilitate the conversion of data from one format to another, often with the
aim of ensuring efficient transmission, secure storage, or accurate
reconstruction. Encoders transform an input signal or data into a coded format,
while decoders reverse this process, converting the coded data back into its
original or a usable form. Their applications are ubiquitous, ranging from the
intricate digital signals underpinning our internet and mobile communications
to the more tangible processes of data compression and error correction, making
them indispensable in nearly every modern technological system.
Part 5.5.1 Encoder
A combinational circuit that produces
n-bit coded combinations of outputs from 2n discrete inputs is
called an encoder.
Example no. 1
Design an encoder-based combinational
circuit that accurately converts a single active octal input (D0 through D7)
into its corresponding 3-bit binary output.
Solution no. 1
Draw
the Truth table.
|
Input |
Output |
|||||||||
|
D0 |
D1 |
D2 |
D3 |
D4 |
D5 |
D6 |
D7 |
x |
y |
z |
|
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
|
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
|
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
|
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
0 |
0 |
|
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
0 |
1 |
|
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
1 |
1 |
0 |
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
Boolean
Expressions:
X
= D4+D5+D6+D7
Y
= D2+D3+D6+D7
Z
= D1+D3+D5+D7
Logic
Circuit:
Part 5.5.1.1 Priority
Encoder
An encoder
circuit that includes a priority function. The operation is such that if two or
more inputs are equal to 1 at the same time, the input having the highest
priority will take precedence.
Example
no. 2
From
the Truth table below, make a combinational logic circuit.
|
D0 |
D1 |
D2 |
D3 |
|
x |
y |
z |
|
0 |
0 |
0 |
0 |
|
x |
x |
0 |
|
1 |
0 |
0 |
0 |
|
0 |
0 |
1 |
|
x |
1 |
0 |
0 |
|
0 |
1 |
1 |
|
x |
x |
1 |
0 |
|
1 |
0 |
1 |
|
x |
x |
x |
1 |
|
1 |
1 |
1 |
Note:
x denotes either 1 or 0.
Solution
no. 2
Boolean
Expressions:
x
= D2 + D3
Y
= D1D2 + D3
Z
= D0 + D1 + D2 + D3
The
Logic Circuit
Part 5.5.2 Decoder
It is a combinational circuit that
converts coded n-bit information to a maximum of 2n unique output
lines. The input code generally has fewer bits than the output code.
Figure 1. 74x139
Dual 2-to-4 Decoder
Part 5.5.2.1 Binary
Decoders as Minterm Generators
The output of an n-to-
Example
no. 3
Design a circuit for the logic function F(x,y,z)=Σ(0,2,3,5)
a.)
Draw the circuit diagram using individual gates.
b.) Draw the decoder-based circuit.
Solution
no. 3
The simplified expression of the function is obtained
as
F=x′z′+x′y+xy′z
Logic circuits:
1.
Using Individual Gates
1.
Using 74x138 3-to-8 Decoder IC
Part 5.5.2.2 BCD
to Decimal Decoder
To
change a BCD number to its decimal equivalent, it is done one decimal digit at
a time. For each decimal integer, a decoder with four inputs and ten outputs is
needed; one decoder is required for each digit in any decimal number to be
decoded. For instance, to decode numbers up to 99 requires two decoders, one
for the units digit and another for the tens digit. An
MSI decoder that can be used to decode 8-4-2-1 code is the 54/7445.
Figure 2. Block
diagram of BCD decoder
For
each of the ten possible inputs, from 0000 10 1001, only one output line is
activated.
Part 5.5.2.3 BCD-to-seven segment
decoder/driver
The
7447 IC is a BCD-to-seven-segment decoder/driver that has four inputs for the
BCD digit. The 4-bit BCD is converted to a seven-segment code with outputs a
through g. The outputs of the 7447 are applied to the inputs of the 7730 (or
equivalent) seven-segment display.
Figure 3. BCD-to-seven-segment
decoder (7447) and seven-segment display (7730) (from: Pearson Education, Inc.)