Saturday, 11 February 2012

Decoders


Combinational circuit is a digital circuit whose output depends only on present input. Below figure shows the block diagram of combinational system.
Decoders:
n to 2n decoder is a combinational circuit with n inputs and 2n output signal, in which at a time only one signal is active.
2 to 4 decoder:
2 to 4 decoder takes 2-bit binary data as input, and produces logic ‘1’ on its binary equivalent number line. For example if A1A0 is “10” then Y2 will be ‘1’ and remaining are ‘0’s.
Truth table:
3 to 8 decoder:
3 to 8 decoder takes 3-bit binary data as input, and produces logic ‘1’ on its binary equivalent number line. For example if A2A1A0 is “101” then Y5 line is active (‘1’) and remaining lines are ‘0’s.
3 to 8 decoder can be implemented using two 2 to 4 decoders having an enable input.
3 to 8 decoder using 2 to 4 decoders:
 3 to 8 decoder using gates:
Truth table:
 
Realizing Boolean function with a decoder:
Since decoder produces all minterms, it is possible to implement any Boolean function with decoder.
  • To implement a function with n variables, select n to 2n decoder.
  • Decoder output produces all minterms
  • Select the required minterms and OR them. This gives the required function.
Ex: realize Boolean function with f (A, B, C) =∑m (1, 4, 5, 7)

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