IC74138(a 3:8 decoder) has 3 enable pins G1, G2A and G2B.
Why are there 3 enable pins and what is the reason for that nomenclature?
Electrical – Pins in IC74138
decoderintegrated-circuit
Related Solutions
Your approach is correct.
This is probably an error, or oversight, in the textbook: the authors forgot to allow for selecting the final decoder, which is what your 9th decoder does.
There's not a standard formula. First, you have to stack up enough decoders to give you the number of output pins you need. Then, you have to "tree up" enough additional decoders to select the output-layer decoders.
There is no problem with your circuit. although I would suggest that you set pull-down resistors on the outputs. that's because the decoders usually set their outputs to high-impedance (high-Z) when they're not enabled. so the output may remain the same on the output node (because of node capacitance) and the wrong value may be read by the device that is reading the current output. making all the outputs pulled-down to GND will eliminate this problem and it will work correctly. Look at the picture below...
You can use a resistor array which is a nine pin element that has 8 resistor inside with a common pin that will be connected to ground! Easy! ;-)
simulate this circuit – Schematic created using CircuitLab
Best Answer
The datasheet for the 74138 explicitly says that the three enable inputs were a design decision that is intended to make it easy to use multiple 74138 chips together to for a one out of 24 or one out of 32 decoder.
Extract from the Datasheet:
With the multiple enables that have different active states (inverted vs. non-inverted,) you can build a one of 24 decoder with no additional inverters in the circuit - saved you a chip full of inverters back in day when they didn't come in SMD form with a single inverter in the package.
This answer from last year shows how the 74138 can be used to build a 1 out of 24 decoder. That example does use additional inverters, but that is because the circuit is doing a bit more than just decoding the inputs - it appears to be using the third enable as a value ot be passed to the outputs. It selects one output, and passes the value at Data-In to that ouput. Were it not for that, there would be no need of the additional inverters, and the 74138s would work together as a 24 output decoder.
Circuit from the linked answer: