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Introduction
 A decoder is a special case of a demultiplexer without
the input line. It is a combination logic circuit that
accepts a set of inputs which represents a binary number
and activates only the output that corresponds to the
input number. A decoder can generate a maximum of 2𝑛
possible minterms with an n-bit binary code. In other
words, a decoder circuit looks at its inputs, determines
which binary number is present there, and activates the
one output that corresponds to that number- all other
outputs remain inactive.

Decoders
 A decoder is a combinational logic circuit with a
number of output lines one of which is active at any
one time.
 The active output line is dependent on the pattern of
the input lines. In general a decoder has n input lines
and 2n output lines. Below is a logic circuit of a 2 to 4
decoder.

Lecture 8 Decoders & Encoders (combinational circuits)

The truth table for the above decoder can be
produced by tracing the input signals from
input to output noting the respective values
of each output line, or can be produced by
substituting the binary values of each input
combination in the above Boolean
expressions.

Decoders have many uses in digital computers.
They can be used to control other circuits.
For example if no changes are needed in other
circuits, the enable line can simply be set to
zero (0).
The other example where decoders are used is
in memory address decoding.

Address Chip
 0000-00FF 0
 0100-01FF 1
 0200-02FF 2
 0300-03FF 3

So each chip requires eight (8) address lines and
these are supplied by the bits 0- 7 bit lines.
The higher- order 2 bits, 8 and 9 are used to
select one of the four chips by using the 2 to 4
decoder.
The outputs of the decoder enable only one of
the four chips at a time.

Address decoding
The block diagram operates as follows:
 To read or store data to a particular memory location,
the 2 to 4 decoder is used to select the chip.
 For example if A8 = 0 and A9 = 0 then chip 0 will be
selected by enable line 0 at the output of the decoder
to a 1.
 The address lines A0 –A7 are then used to identify the
unique memory location where data can be written to
or read from. Only one chip operate at a time in the
above arrangement.

Encoders
An encoder is a logic circuit that converts information
or data from one form to another or from one code
to another, for example changing an octal code
number to a binary number.
The encoders are exactly the opposite of decoders.
In general an encoder has m inputs and n output lines.
Of the m input line only one is activated at a time.

Introduction
 An encoder is a multiplexer without its single output
line. It is a combinational logic function that has 2𝑁
(or
fewer) input lines and 𝑛 output lines, which correspond
to𝑁 selection lines in a multiplexer. The 𝑛 output lines
generate the binary code for the possible 2𝑁 input lines.
For a an encoder with 𝑁 = 2, there are four input lines
and two output lines.
 Figure 4-12 is the general diagram for an encoder with
𝑀 inputs and 𝑁 outputs. The inputs here active HIGH,
which means they are normally LOW.

 4-12 General encoder diagram

 4 to 2 Encoder
 A 4 to 2 encoder has four inputs 𝑌3, 𝑌2, 𝑌1 and 𝑌0 and
two outputs 𝐴1 and 𝐴0. A block diagram of 4 to 2
Encoder
 is shown in the following figure 4-13.
 Fig. 4-12 4 to 2 encoder diagram

 At any time, only one of these 4 inputs can be ‘1’ in
order to get the respective binary code at the output.
The Truth table is shown below.

 From Truth table, we can write the Boolean functions for
each output is as follows;
 A1=Y3+Y2
 A0=Y3+Y1
 Implementation of the above Boolean expressions is
shown in the following circuit diagram.

 Fig 4-13 4 to 2 Circuit diagram

Encoders can also be used for security
(data inscription) and saving memory
space (data compression). An example of
a basic encoder logic circuit is shown
below:

Octal to Binary Encoder
 Octal to Binary Encoder
 An octal to binary encoder would have eight input
lines, each representing an octal digit, and three
output lines representing the three-bit binary
equivalent. The eight inputs are 𝑋7 to 𝑋0 and three
outputs 𝑌2, 𝑌1 and 𝑌0. Octal to binary encoder is
nothing but 8 to 3 encoder. The block diagram is
shown in Fig. 4-14 below.

Octal to Binary Encoder block diagram

 The eight input lines would have 28 = 256 possible
combinations. However, in the case of an octal-to-
binary encoder, only eight of these 256 combinations
would have any meaning. The remaining combinations
of input variables are ‘𝑑𝑜𝑛’𝑡 𝑐𝑎𝑟𝑒’ input combinations.
Also, only one of the input lines at a time is in logic ‘1’
state.

Disadvantages of an encoder
 There is an ambiguity, when all outputs of encoder are
equal to zero. Because, it could be the code
corresponding to the inputs, when only least significant
input is one or when all inputs are zero.
 If more than one input is active High, then the encoder
produces an output, which may not be the correct code.
For example, if both 𝑌3 and 𝑌6 are ‘1’, then the encoder
produces 111 at the output. This is neither equivalent
code corresponding to 𝑌3, when it is ‘1’ nor the
equivalent code corresponding to 𝑌6, when it is ‘1’.

 So, to overcome these difficulties, we should assign
priorities to each input of encoder. Then, the output of
encoder will be the binary code corresponding to the
active HIGH inputs, which has higher priority. The
encoder is known as priority encoder.
 When more than one input is simultaneously active,
the input with the highest priority is encoded.

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Lecture 8 Decoders & Encoders (combinational circuits)

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