System Design Applications

Exclusive-OR gates can be used to perform a controlled inversion of a data word.
The controlled inversion combined with an additional 1 on the carry input of the LSB of a set of full-adders will give the two's-complement of a number.
Subtraction can be accomplished by taking the two's-complement of a number and adding.
BCD addition can be accomplished also with full-adders.
One set of adder circuits is used to do the original addition. Some addition logic is necessary to detect a carry or an illegal number. A second set of adder circuits is then used to add six to the first sum.
The 74HC583 is a single chip that will perform all the necessary steps in order to add 2 BCD digits.