Full Subtractor – Truth table & Logic Diagram

A subtractor is a digital logic circuit in electronics that performs the operation of subtraction of two number. Subtractors are classified into two types: half subtractor and full subtractor.

A full subtractor (FS) is a combinational circuit that performs a subtraction between two bits, taking into account borrow of the lower significant stage. This circuit has three inputs and two outputs. The three inputs are A, B and C, denote the minuend, subtrahend, and the previous borrow, respectively. The two outputs are the difference (A−B−C) and borrow.

full-subtractor-block-diagram
Fig. 1 FS block diagram

The truth table of the full subtractor Circuit is shown in figure 2.

full-subtractor-truth-table
Fig. 2 Truth table

Implementation of Full Subtractor

Logical expression for Difference,

Logical expression for borrow,

full-subtractor-logic-diagram
Fig.3 Logic diagram for FS

The FS works by combining the operations of basic logic gates, with the simplest form using one XOR, one OR, one NOT & three AND gate.

Note:

1. FS can be implemented with two half subtractor and one OR gate.

full-subtractor-using-two-half-subtractor-or-gate
Fig.4  FS using two half-subtractor and one OR gate

2. Minimum number of NAND Gate required implementing FS = 9

3. Minimum number of NOR Gate required implementing FS = 9

4. FS can be implemented by a combination of one 3×8 decoder and two OR gate.

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