What is a full subtractor truth table

A full subtractor truth table displays all possible input combinations and their corresponding outputs for a full subtractor circuit, which performs binary subtraction of three inputs: the minuend bit (A), subtrahend bit (B), and borrow-in from the previous position (Bin), producing two outputs: the difference bit (D) and borrow-out bit (Bout). The truth table has eight rows representing all combinations of three binary inputs (000, 001, 010, 011, 100, 101, 110, 111), showing the resulting difference and borrow-out for each.

The full subtractor truth table is: when inputs A, B, Bin are (0,0,0) → D=0, Bout=0; (0,0,1) → D=1, Bout=1; (0,1,0) → D=1, Bout=1; (0,1,1) → D=0, Bout=1; (1,0,0) → D=1, Bout=0; (1,0,1) → D=0, Bout=0; (1,1,0) → D=0, Bout=0; (1,1,1) → D=1, Bout=1. The difference bit follows the pattern D = A XOR B XOR Bin (same as addition's sum function), while borrow-out is Bout = (NOT A AND B) OR (NOT A AND Bin) OR (B AND Bin), which is 1 when you need to borrow from the next higher bit. In practice, modern computers typically don't use dedicated subtractor circuits—instead, they perform subtraction using addition and two's complement representation (subtracting B from A is equivalent to adding A plus the two's complement of B). However, understanding full subtractors is valuable for learning digital design fundamentals, and they appear in specialized applications where dedicated subtraction circuits are preferred. The full subtractor truth table parallels the full adder but with borrow logic replacing carry logic, demonstrating how binary arithmetic operations translate into hardware through systematically defined input-output relationships implemented via logic gates.