Digital Electronics/Mathematic and Logic Operations/Digital Subtractor

Half Subtractor The half-subtractor is a combinational circuit which is used to perform subtraction of two bits. It has two inputs, X (minuend) and Y (subtrahend) and two outputs D (difference) and B (borrow). Truth Table The truth table for the half subtractor is given below. http://www.shef.ac.uk/physics/teaching/phy107/logicsub.html "Subtraction using Logic gates" X Y D B 0 0 0 0 0 1 1 1 1 0 1 0 1 1 0 0 From the above table one can draw the Karnaugh map for "difference" and "borrow". Full Subtractor The full subtractor is a combinational circuit which is used to perform subtraction of three bits. It has three inputs, X (minuend) and Y (subtrahend) and Z (subtrahend) and two outputs D (difference) and B (borrow). Truth Table The truth table for the full subtractor is given below. http://www.shef.ac.uk/physics/teaching/phy107/logicsub.html "Subtraction using Logic gates" X Y Z D B 0 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 1 1 0 1 1 0 0 1 0 1 0 1 0 0 1 1 0 0 0 1 1 1 1 1 So, logic equations are D = (X xor Y)xor Z, B = (Z and (not(X xor Y)))or ((not X)and Y) References