Q. What do you mean by Decoders?

Decoder transforms one kind of coded information to other form. A decoder has n inputs and one enable line (sort of selection line) and 2ⁿ output lines. Let's see an example of 3:8 decoder that decodes a 3 bit information and there is just one output line that gets value 1 or in other words out of 2³ = 8 lines just 1 output line is selected. So depending on selected output line information of 3 bits can be identified or decoded.           

Figure:  3×8 decoder

Please be certain while constructing logic figure wherever values in the truth table are appearing as zero in input and one in output the input must be fed in complemented form for example first 4 entries of truth table comprises 0 in I₀ position and therefore I₀ value 0 is passed by a NOT gate and fed to AND gates 'a', 'b', 'c' and'd' that implies that these gates shall be triggered/selected only if I₀ is 0. If I₀ value is 1 then not any of the top 4 AND gates can be selected. Similar kind of logic is valid for I₁. Please note output line selected is named 000 or 010 or 111 etc. Output value of only one of lines would be 1. These 000, 010 denotes the label and imply that if you have these I₀ I₁ I₂ input values labelled line would be activated for the output. Enable line is a good resource for joining two 3×8 decoders to make one 4×16 decoder.