In this circuit's description, It is given that we can extend the circuit easily to generate up to 12 DTMF signals. How can that be done?
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The four outputs actually give a binary code out, so there are 16 possible combinations. This circuit only uses the codes where only 1 but is high:
0001 0010 0100 1000
If you would use one of the other codes you would switch 2 or more outputs simultaneously.
What you want is a 4-to-16 demultiplexer, like the 74HC154. This will give you a low pulse on one of the 16 outputs when the corresponding DTMF code is sent. The original schematic gives an active high pulse. This means that either you have to invert the polarities of all the outputs, or that the output will only switch when the key is released instead of being pressed.
For the transmitter you simply have to add extra buttons in the rows/columns matrix.
At the end of the circuit description it talks about what needs to be done to increase the number of channels.
The transmitter would need the corresponding buttons added to it, and the receiver would need a 4 to 16 multiplexer attached (note inversion mentioned by Stephen, maybe a negative edge triggered flip flop could be used - random example in DIP here) so if the 4 outs are e.g. 0110, rather than turning switch 2 and 4 on, it will turn only switch 6 on (2 + 4 = 6)