Below is 4 bit binary full adder and subtractor I made in logisim, at first it's a 4 bit adder, but if you press the Cin button, The Cout LED turns on, and it turns into a 4 bit subtractor, and you have to input the A values first, and it subtracts the B values you put in afterwards. A0 and B0 and S0 are the least significant bits and A3 and B3 and S3 are the most significants. The outputs are LEDs. all the steps are shown. I ask that you please with either clear neat handwriting or typed text (if I can't read it's useless), give a very detailed explanation about the whole system, a technical explanation, truth tables, the underlying logic behind it all, etc. without leaving ANYTHING out, please don't rush, I don't want confusing unorganized stuff, it just happened, someone just sent me unreadable writing with very hard to understand unorganized stuff, he clearly rushed, as if you were writing a report, because I will use the knowledge you give to prepare my own unique report, so be as detailed as possible, and please don't copy and paste from the internet, unless it's a very general thing that you would also write yourself. This is very important for me so please help me out.

A FULL ADDER:

THE NEXT STEP:

THE FINAL FORM:

A SO BION Cino Cout Cino AOI0 SO Full Adder A10 OS1 Full Adder A20 OS2 Full Adder Os3 Full Adder O Cout BOO B1 0 B2 B310 Cino AO OI A10 A2 0 SO A30 S1 4 Bit Binary Calculator (Adder & Subtractor) S2 BOO S3 B110 B20 B3 0 Cout