A decoder is similar to demultiplexer, with one exception and there is no data input. The only input are the control input ABCD. In this logic circuit only 1 of the 16 output lines is high and therefor it is called 1-OF-16 Decoder.
Let control input ABCD=0001, so only Y1 AND has all input high, therefore only Y1 is high. The subscript of Y1 is 1, means when you conver ABCD=0001 binary nibble into decimal answer will be 1.Similarly when ABCD=0100, only Y4 AND gate has all high input , as a result Y4 goes high. The subscript of Y4 is 4, so when you conver ABCD=0100 into decimal, it will be 4.
Verify it using following calculator
Thus subscript of high output is always equals the decimal equivalent of ABCD. Therefore circuit is also called a binary-t0-decimal decoder.
IC-74154 as Decoder-Demultiplexer:
As shown in above pin diagram of IC-74154, DATA and STROBE inputs are grounded. The bubbles at the output shows that the output is low when it is active. Say binary input is ABCD=0111, then Y7 output is low, while all other outputs are high.