Full Subtractor in Digital Logic Last Updated : 10 Apr, 2025 Comments Improve Suggest changes Like Article Like Report A Full Subtractor is a combinational circuit used to perform binary subtraction. It has three inputs:A (Minuend)B (Subtrahend)B-IN (Borrow-in from the previous stage)It produces two outputs:Difference (D): The result of the subtraction.Borrow-out (B-OUT): Indicates if a borrow is needed for the next stage.The full subtractor is essential because a half-subtractor can only subtract the least significant bit (LSB) of binary numbers. However, if a borrow is generated during the subtraction of the LSBs, it will affect the subtraction in the next stages. A full subtractor handles this situation by considering the borrow from the previous stage, ensuring accurate subtraction even when a borrow is present.The full subtractor is used to subtract binary numbers with borrow handling, making it suitable for multi-bit subtraction in digital circuits like Arithmetic Logic Units (ALUs). Full Subtractor in Digital LogicTruth Table of Full SubtractorInputOutputABBinDBout0000000111010110110110010101001100011111K-Map for Full SubtractorFrom above table we can draw the K-Map as shown for "difference" and "borrow". K-Map for DifferenceLogical expression for difference The basic expression is:D = A'B'Bin + A'BBin' + AB'Bin' + ABBinFactoring common terms:D = Bin(A'B' + AB) + Bin'(AB' + A'B)Recognizing XOR and XNOR properties:A'B' + AB = A XNOR BAB' + A'B = A XOR BSubstituting these values:D = Bin(A XNOR B) + Bin' (A XOR B)Using XNOR identity:D = Bin ⊕ (A ⊕ B)Thus, the final simplified expression for the difference in a full subtractor is:D = (A ⊕ B) ⊕ BinK-Map for BorrowLogical expression for borrow The borrow (Bout) output is derived as follows:The basic expression:Bout = A'B'Bin + A'BBin' + A'BBin + ABBinFactoring common terms:Bout = A'Bin(B + B') + A'B(Bin + Bin') + BBin(A + A')Simplifying:Bout = A'Bin + A'B + BBinAlternatively, using another approach:Bout = A'B'Bin + A'BBin' + A'BBin + ABBinFactoring common terms:Bout = Bin(AB + A'B') + A'B(Bin + Bin')Using XOR and XNOR properties:AB + A'B' = A XNOR BSubstituting these values:Bout = Bin(A XNOR B) + A'BUsing XNOR identity:Bout = Bin (A XOR B)' + A'BThus, the final simplified expression for borrow in a full subtractor is:Logic Circuit for Full Subtractor Logic Circuit for Full SubtractorImplementation of Full Subtractor using Half Subtractors2 Half Subtractors and an OR gate is required to implement a Full Subtractor.Implementation of Full Subtractors using Half Subtractor Comment More infoAdvertise with us Next Article Parallel Adder and Parallel Subtractor H Harshita Pandey Follow Improve Article Tags : Misc GATE CS Digital Logic Practice Tags : Misc Similar Reads Digital Electronics and Logic Design Tutorials Digital Electronics and Logic Design are key concepts in both electronics and computer science. 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