A full subtractor is a combinational circuit that performs subtraction of three bits. This circuit has three inputs the minuend A, subtrahend B, and borrow in B_{in}. B_{in} is the borrow of the previous adjacent lower minuend bit. This B_{in} is also subtracted from A-B. A full subtractor has two outputs, D and B_{out}, represents Difference and Borrow Out respectively.

Truth table of a full subtractor is,

A

B

B_{in}

D

B_{out}

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

The logic expression for full subtractor can be derived from the truth table using the K-Map technique.

$${D=(A \oplus B) \oplus B_{in}}$$

Expression for B_{out} can be again simplified as follows