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## Computer organization Notes--Full Subtractor

The disadvantage of a half subtractor is overcome by full subtractor. A full subtractor, just like full adder, takes into consideration that 1 might have been borrowed by the lower significant bit from the current bit. The block diagram of a full subtractor can be drawn as follows:

Hence this circuit of full subtractor is a combinational circuit with three inputs A,B,C, where C is previous borrow and A is the bit from which B will be subtracted and two output D and Bout. A is the 'minuend', B is 'subtrahend', C is the 'borrow' produced by the previous stage, D is the difference output and Bout is the borrow output if taken from the next higher significant bit.
The truth table for Full Subtractor is

The Circuit Diagram for Full Subtractor is

From the Truth Table The Difference and Borrow will written as
Difference=A'B'C+A'BC'+AB'C'+ABC
Bout = A'B'C+A'BC'+A'BC+ABC
These expressions can be simplified using k-maps as follows-
For Difference D                For Borrow Bout Simplified functions are represented as
Difference=A'B'C+A'BC'+AB'C'+ABC
Bout = A'B'C+A'BC'+A'BC+ABC
Reduce it like adder Then We got
Difference=A B C
Borrow=A'B'C+A'BC'+A'BC+ABC
=A'B'C+A'BC'+A'BC+A'BC+A'BC+ABC ----------> A'BC=A'BC+A'BC+A'BC
=A'C(B'+B)+A'B(C'+C)+BC(A'+A) Borrow=A'C+A'B+BC
The logical diagram for Full subtractor can be drawn as follows
For Difference D

For Borrow Bout

Here, we can see that logical function for output D in case of full subtractor is same as the output S in Full Adder. Also, the output Bout is similar to C in full adder except that input variable A is complimented.
Full Subtractors using two Half Subtractors

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