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 2

^{n}decoder is a combinational circuit with n inputs and 2^{n}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 2
^{n}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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