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.

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.

So, logic equations are D = (X xor Y)xor Z, B = (Z and (not(X xor Y)))or ((not X)and Y)