Decoders in digital electronics

Decoders in digital electronics...
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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 ‘2 n ’ output lines Eg : if n=2 then Decoder is having 2 i /p lines and 2 2 =4 o/p lines Similarly if n=3 then Decoder is having 3 i /p lines and 2 3 =8 o/p lines if n=4 then Decoder is having 4 i /p lines and 2 4 =16 o/p lines lines

4. 2 to 4 De coder We know that if n=2 then decoder is having 2 i /p lines and 2 2 =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 D 3 D 2 D 1 D D D 1 D 3 D 2

5. Boolean Exp: D 3 =E.A 1 .A D 2 =E.A 1 .A ′ D 1 =E.A 1 ′.A D =E.A 1 ′.A ′ LOGIC CIRCUIT D 3 D 2 D 1 D 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 and 2 3 =8 o/p lines A B C

7.  Truth table of 3 to 8 line decoder D 7 D 5 D 4 D 3 D 2 D 1 D D 6 D 1 = A’ B’ C D 2 = A’ B C’ D 3 = A’ B C D 4 = A B’ C’ D 5 = A B’ C D 6 = A B C’ D 7 = A B C D = 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, A 1  & A  and four outputs, D 3  to D . Whereas, 3 to 8 Decoder has three inputs A 2 , A 1  & A  and eight outputs, D 7  to D . 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. D 7 D 6 D 5 D 4 D 3 D 2 D 1 D

11. A1 A2 A0 D 1 = A2’ A1’ A0 D 2 = A2’ A1 A0’ D 3 = A2’ A1 A0 D 4 = A2 A1’ A0’ D 5 = A2 A1’ A0 D 6 = A2 A1 A0’ D 7 = A2 A1 A0 D = A2’ A1’ A0’

12. D D 1 D 2 D 3 D 4 D 5 D 6 D 7  Logic circuit diagram

13. 4 to 16 Decoder If n=4 then Decoder is having 4 i /p lines and 2 4 =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 A 2 , A 1  & A  and eight outputs, D 7  to D . Whereas, 4 to 16 Decoder has four inputs A 3 , A 2 , A 1  & A  and sixteen outputs, D 15  to D 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. D 7 D 6 D 5 D 4 D 3 D 2 D 1 D D 15 D 14 D 13 D 12 D 11 D 10 D 9 D 8 Block Digram

15. A 3 A 2 A 1 A D D 1 D 2 D 3 D 4 D 5 D 6 D 7 D 8 D 9 D 10 D 11 D 12 D 13 D 14 D 15 Write Boolean Expressions from D to D 15

16. Logic Circuit Try to Draw this on your own

17. In Next Class Multiplexers De Multiplexers

18. A