I was supposed to make a full adder circuit of two 1 bit numbers using any amount of 1/4 demultiplexers and only one NOR gate with arbitrary number of inputs.I have no idea how to do this.Is such thing even possible?With just one NOR gate you can have either a carry bit output or a sum bit output, not both.How does one approach a problem like this one?What's the general procedure?
A dumb, but a universal approach would be to use the demux to implement a universal gate such as
NOR. Each demux can implement 4 different functions of two variables on the following way:
|^^^^^^| | |--- A'B' 1 ---| |--- A'B | |--- AB' | |--- AB |______| | | A B
A'B'. It is the same as
(A+B)', which is...
So this proves that the task is possible and doable (or a stronger claim - that any logical function can be implemented using 1-4 demuxes).
As a bonus you can get an
AND gate and two components of
XOR out of it, which will significantly reduce the number of such a a units in the final circuit.
If you are not allowed to use constants such as
1, you can utilize the provided single
NOR gate connected to the two of the demux outputs as following:
|^^^^^^| | |---______ A ---| |---\ NOR \____ | |---/_____/ | |--- |______| | | A A
Since these two outputs will be low for any
NOR will output