# How to implement unsigned subtraction using 2's complement?

I want to implement unsigned subtraction using 2's complement. I arrived to this, where if I have 2 4-bit binary numbers A and B, I transform B to 2's complement (let us name it B' so we don't get confused) and then add A to B'and I get the result C. This was the easy part for me.

Then if the final carry out is "0" I should transform C to 2's complement and add a "-" sign, but if the carry out is "1" I just don't adjust anything. And this is where it got me. I don't know how to implement it and I should put a led in the final result to let know if the sign is "+/-".

I think I should put a 2-to-1 multiplexer where the select input will be the carry out of the circuit I posted.

And by the way, my implementation is correct, whenever I put random values and then calculate those by hand I get the same result.

(The program I used is called "logicCircuit".

So this is what I got to.(After editing my post) The circuit above is my main circuit.  These 2 pictures above are just zoomed in photos of the circuit

Now my question is, can I do something so I can get only one result. For example if the carry is "0" The multiplexer gives me the correct result, but in the same time I am getting a result in the upper part of my circuit which is the part that should give me a result whenever the carry is "1" and vice versa.

The gray bubble are leds so when the result is 1, the led lights up.

• RE " if I have 2 4-bit binary numbers A and B, I transform B to 2's complement ", how many bits is the 2's complement result? If it's 4 bits, what do you do if B > 7? – The Photon May 2 '20 at 14:53
• @ThePhoton the 2's complement result is also 4 bits. I don't want any of the inputs to be higher than 4-bits. – P_M May 2 '20 at 14:59
• @PeterMurr Just in case you aren't thinking about it, make sure that if you complement an input, that you also either complement the carry-in or set it to 1 depending on the operation you desire. – jonk May 2 '20 at 19:02

You have a multiplexer. One input to the multiplexer is the output of the addition (A+B'). The other input of the multiplexer is the 2's complement of that (A+B')'. (Where we're using ' to indicate the 2's complement operation rather than simple inversion)