What is a Full Subtractor?
A full subtractor is an arithmetic circuit that performs a subtraction between two bits, considering that a lower significant stage may have borrowed a '1'. Thus a full subtractor has three inputs and two outputs. The full subtractor block diagram is shown below.
Truth Table of Full Subtractor
The two inputs are A and B, and the third input is input as C. The output carry is designated as b(borrow), and the normal output is designated as d, which is the difference. The truth table of a full subtractor is represented as given below:
Output Equation of Full Subtractor
From the above truth table, the map for the outputs of the full subtractor is shown below, and the logical expression for the difference and borrow is as below:
Implementation of Full Subtractor Circuit
From the above expression, a full subtractor circuit can be realized in SOP form or with two half subtractors and an OR gate, as shown below:
The ANSI/IEEE standard logic diagram of the full subtractor is shown below:
The full subtractor can also be realized using a universal logic gate that is either only NAND gates or only NOR gates. The total number of NAND gates/Nor gates required to implement a full subtractor equals "9".