decoder and encoder

1. BY UNSA SHAKIR
Decoders and Encoders
Digital Systems

2. Lecture
Example
• Implement F = XYZ + YZ with
• 8:1 MUX
• 4:1 MUX
• Establish function in a truth table and design
circuit diagram.

3. Lecture
Example
• Consider F(A,B,C) = m(1,3,5,6). We can
implement this function using a 4-to-1 MUX as
follows.
• Establish function in a truth table and design
circuit diagram.

4. Lecture
MUX Example (cont.)
A B C F
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 1
1 1 1 0
When A=B=0, F=C
When A=0, B=1, F=C
When A=1, B=0, F=C
When A=B=1, F=C’

5. Lecture
MUX implementation of F(A,B,C) =m(1,3,5,6)

6. Lecture
Example
• Consider F(A,B,C) = m(1,3,4,11,12,13,14,15).
We can implement this function using a 8-to-1
MUX as follows.
• Establish function in a truth table and design
circuit diagram.

7. Lecture
A larger Example

8. Lecture
Encoder/Decoder
ENCODER- a digital circuit that produces a binary
output code depending on which of its inputs are
activated.
DECODER- a digital circuit that converts an input
binary code into a single numeric output.
A0
A1
A2
A3
A4
A5
A6
A7
ENCODER
O0
O1
O2
A0
A1
A2
O0
O1
O2
O3
O4
O5
O6
O7
DECODER

9. Lecture
Encoders
• Binary code of N digits can be used to store
2N distinct elements of coded information.
• Encoders convert 2N lines of input into a code of N
bits and

10. Lecture
Encoder Example
Lecture Digital Systems
 In encoder circuit only one input may be set high (1) at a
certain time.
 The output is a 2-bit number.
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
I3 I2 I1 I0 Y1 Y0
I0
I1
I2
I3
Y1
Y0
• Example: 4-to-2 binary encoder

11. Lecture
Encoder Example
• Example: 8-to-3 binary encoder (octal-to-binary)
A0 = D1 + D3 + D5 + D7
A1 = D2 + D3 + D6 + D7
A2 = D4 + D5 + D6 + D7

12. Lecture
Encoder Example (cont.)

13. Lecture

14. Lecture
Encoder Example
• Example: 10-to-4 binary encoder
(decimal-to-binary)

15. Lecture
• Y0 = D1 + D3 + D5 + D7 + D9
• Y1 = D2 + D3 + D6 + D7
• Y2 = D4 + D5 + D6 + D7
• Y3 = D8 + D9
• Example: 10-to-4 binary encoder
(decimal-to-binary)

16. Lecture
• Example: 10-to-4 binary encoder
(decimal-to-binary)

17. Lecture
• Example: 10-to-4 binary encoder
(decimal-to-binary)

18. Lecture
Decoders

19. Lecture
Binary Decoders
Lecture Digital Systems
 Binary decoders convert an n-bit input to a single output. It
uses its n-bit input to determine which of the 2n outputs will
be uniquely activated.
 Binary decoders can be developed using AND or OR Gates.
 Later on, binary decoders can be implemented in logic
circuits.
 The outputs of a decoder are minterms. That is why
decoders are sometimes called as minterm generators.
 We can easily use a decoder to implement any sum of
minterms expression.
 Note: A minterm is a Boolean expression resulting in 1 only
for the output of a single row (in a truth table) or a single cell
(in a Karnaugh map), and 0s for all other row or cells,
respectively.

20. Lecture
2-to-4 Binary Decoder
Lecture Digital Systems
 A circuit of 2-to-4 binary decoder is shown below.
Binary
Decoder
2 inputs 4 outputs
Enable
 The truth table shows that for any given input combination,
exactly one output will turn to 1.
 The enable must be set to 1 to get an output.

21. Lecture
3-to-8 Binary Decoder
Lecture Digital Systems
X Y Z F0 F1 F2 F3 F4 F5 F6 F7
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
 Try to understand the logic circuit of
3-to-8 binary decoder below.
Binary
Decoder
3 inputs 8 outputs
Enable

22. Lecture
Combinational Circuit Design with Decoders
Example Realize F (X,Y,Z) = Σ (1, 4, 7) with a decoder:

23. Lecture
Decoder as a Logic Building Block

24. Lecture
Decoder as a Logic Building Block

25. Lecture
TEST
A0
A1
A2
A3
A4
A5
A6
A7
ENCODER
O0
O1
O2
O3
A8
A9
INPUT O3 O2 O1 O0
A1=1
A4=1
A6=1
A8=1

26. Lecture
A0
A1
A2
O0
O1
O2
O3
O4
O5
O6
O7
DECODER
O8
O9
A3
A3 A2 A1 A0 OUTPUT
0 0 0 0
0 1 0 1
0 1 1 1
1 0 0 1
TEST

27. Lecture
ANSWER THE FOLLOWING QUESTIONS WITH ONE OR MORE OF THESE
WORDS: MUX, DEMUX, ENCODER, DECODER.
A. Has more inputs than outputs. ENCODER, MUX
B. Uses select inputs. MUX, DEMUX
C. Can be used in parallel-to-serial conversion.
MUX
D. Produces a binary code at its output.
ENCODER
E. Only one of its outputs is activated at one time. DEMUX, DECODER
F. Used to route input signals to one of several outputs. MUX
G. Used to generate arbitrary logic functions. MUX, DEMUX
H. 3 line-to-8 line or binary to octal. DECODER
I. Data Selectors are also MUX