The main difference between the Full Subtractor and the previous Half Subtractor circuit is that a full subtractor has three inputs. Then we need to produce what is called a “full binary subtractor” circuit to take into account this borrow-in input from a previous circuit. One major disadvantage of the Half Subtractor circuit when used as a binary subtractor, is that there is no provision for a “Borrow-in” from the previous circuit when subtracting multiple data bits from each other. Then all that is needed to convert a half adder to a half subtractor is the inversion of the minuend input X. The two Boolean expressions for the binary subtractor BORROW is also very similar to that for the adders CARRY. If we compare the Boolean expressions of the half subtractor with a half adder, we can see that the two expressions for the SUM (adder) and DIFFERENCE (subtractor) are exactly the same and so they should be because of the Exclusive-OR gate function.
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