Is it possible to make a circuit that can convert binary to decimal?
Yes, it is possible.

If your input is straight binary (not BCD) and all you have is transistors and logic gates then you will need to start by creating the truth tables for the function you need. The inputs to the truth tables will be the bits of the binary value; the outputs will be the bits of the decimal value.

Once you have the truth tables you can try to use Karnaugh maps or Quine-McCluskey techniques for minimization.

Another alternative would be to use your transistors to build a ROM that did the conversion. The address lines to the ROM would be your binary bits and the data lines coming out would be the desired decimal bits.

Either way, you should probably sharpen your wirestrippers first.