How we can make 4-bit Subtractor using gates

Hey Friends! When we talk about subtraction in binary, it is generally performed using addition of 2's complements of the number to be subtracted. Suppose we want to subtract A & B (i.e. A-B) then this operation is performed as A + (2's complement of B). 1's complement of the binary number is simply the complement of number (change 1 to 0 & vice versa) and adding 1 to 1's complement provides 2's complement of the number. Now the operation mentioned in the first step 1 is achieved using XOR gate. If one input of XOR gate is logic 0 then the output will be same as of the other input. Suppose if one input is A and other input is logic 0 to XOR gate then output will be A. If one input of XOR gate is logic 1 then the output will be complement of the other input. Suppose if one input is A and other input is logic 1 to XOR gate then output will be A's 1’s complement. Now we just need to add 1 to get 2's complement of the number. This is achieved in 4 bit subtractor using carry in I.e. C0. Let us understand this using the logic diagram of the 4 bit subtractor. If we keenly observe the diagram then we will come to know that the carry C0 to first FA is also input to XOR gates. This is because when M is logic 1, XOR will provide 1's complement and to add 1 to produce 2's complement output , the same carry is used. Hence output S will be subtraction of A & B and C's are respective carry.