# Binary Adder/Subtractor

Subtraction of binary numbers can be carried out  by using the addition of 2’s complement of subtrahend to the minuend. In this operation If the MSB  of addition is a ‘0’, then the answer is correct and if MSB is ‘1’,  then answer is having negative sign. Hence, by using full adders subtraction can be carried out.

Figure above the realization of 4 bit adder-subtractor.  From the figure it can be seen that,  the bits of the binary numbers are given to full adder through the XOR gates.  The control input is controls the addition or subtraction operation.

When the SUBTRACTION input is  logic ‘0’ , the B3 B2 B1 B0 are passed to the full adders.  Hence, the output of the full adders is the addition of the two numbers.

When the SUBTRACTION input is  logic ‘1’ ,  the B3 B2 B1 B0 are  complemented. Further,  the SUBTRACTION logic ‘1’  input is also work as Cin for the LSB full adder, due to which 2’s complement addition can be carried out.  Hence, the outputs of the full adders in this case is the subtraction of two numbers.