Decoders in digital electronics... You can watch my lectures at: Digital electronics playlist in my youtube channel: https://www.youtube.com/channel/UC_fItK7wBO6zdWHVPIYV8dQ?view_as=subscriber My Website : https://easyninspire.blogspot.com/

1. DECODERS

2. Today's Topic
Combinational Logic Circuits
• Decoders

3. Decoder
• In general an Decoder is a device or crkt. that converts data from one
format to another. Performs Exact opp. Operation of Encoder.
• In Digital circuits Decoder is a combinational circuit that is used to
convert binary form to other.
• It has maximum of ‘n’ input lines and ‘2n’ output lines
• Eg: if n=2 then Decoder is having 2 i/p lines and22 =4 o/p lines
Similarly if n=3 then Decoder is having 3 i/p lines and23 =8 o/p lines
if n=4 then Decoder is having 4 i/p lines and 24 =16 o/p lines lines

4. 2 to 4 Decoder
• We know that if n=2 then decoder is having 2 i/p lines and22 =4 o/p
lines that means it is a 2 to 4 Decoder
• Consider 2 to 4 Decoder
• The block diagram is
• E is Enable
Truth Table is
D3
D2
D1
D0
D0D1D3 D2

5. Boolean Exp:
D3=E.A1.A0
D2=E.A1.A0′
D1=E.A1′.A0
D0=E.A1′.A0′
LOGIC CIRCUIT
D3
D2
D1
D0
One of these four outputs will
be ‘1’ for each combination of
inputs when enable, E is ‘1’.

6. 3 to 8 Decoder
• 3 to 8 Decoder is having 3 i/p lines and23 =8 o/p lines
A
B
C

7. Truth table of 3 to 8 line decoder
D7 D5 D4 D3 D2 D1 D0D6
D1 = A’ B’ C D2 = A’ B C’
D3 = A’ B C D4 = A B’ C’
D5 = A B’ C D6 = A B C’
D7 = A B C D0= A’ B’ C’
Implementation

8. Logic Circuit

9. Implementing with 2 to 4 Decoders
• let us implement 3 to 8 decoder using 2 to 4 decoders.
• We know that 2 to 4 Decoder has two inputs, A1 & A0 and four outputs, D3 to D0.
Whereas, 3 to 8 Decoder has three inputs A2, A1 & A0 and eight outputs, D7 to D0.
 Number of lower order decoders required for implementing higher order decoder
using the following formula.
 Required number of lower order decoders =m2/m1
 m1 is the number of outputs of lower order decoder.
 m2 is the number of outputs of higher order decoder.
• Here, m1 = 4 and m2 = 8. Substitute, these two values in the above formula.
• Required number of 2 to 4 decoders =8/4=2

10. D7
D6
D5
D4
D3
D2
D1
D0

11. A1A2 A0
D1 = A2’ A1’ A0 D2 = A2’ A1 A0’
D3 = A2’ A1 A0 D4 = A2 A1’ A0’
D5 = A2 A1’ A0 D6 = A2 A1 A0’
D7 = A2 A1 A0 D0= A2’ A1’ A0’

12. D0
D1
D2
D3
D4
D5
D6
D7
Logic circuit diagram

13. 4 to 16 Decoder
• If n=4 then Decoder is having 4 i/p lines and 24 =16 o/p lines lines
• Here I’m designing 4 to 16 decoder using 3 to 8 decoder circuits.
• We know that 3 to 8 Decoder has three inputs A2, A1 & A0 and eight
outputs, D7 to D0. Whereas, 4 to 16 Decoder has four inputs A3, A2,
A1 & A0 and sixteen outputs, D15 to D0
• Here, m1 = 8 and m2 = 16. Substitute, these two values in the
formula.
• Required number of 2 to 4 decoders =m2/m1= 16/8=2

14. D7
D6
D5
D4
D3
D2
D1
D0
D15
D14
D13
D12
D11
D10
D9
D8
Block Digram

15. A3 A2 A1 A0 D0 D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D11 D12 D13 D14 D15
Write Boolean Expressions from D0 to D15

16. Logic Circuit
Try to Draw this on
your own

17. In Next Class
• Multiplexers
• De Multiplexers

18. • A