SECTION II-2: Logic Design Using Gates

If we add two binary digits there are four possible outcomes:

A simple Logic design to add two Binary digits
	Carry	Sum
0 + 0 =	0	0
0 + 1 =	0	1
1 + 0 =	0	1
1 + 1 =	1	0

When we add 1 + 1 we get 0 with a carry to the next higher place. We will need to determine the sum and the carry for this design. The sum column above matches the output for the XOR function, and that the carry column matches the output for the AND function. Below demonstrated a simple adder implemented with XOR and AND gates, and demonstrated the same logic circuit implemented with AND and OR gates and inverters.

Two Implementations of a Half-Adder
Half-Adder Using XOR and AND	Half-Adder Using AND, OR, Inverters

Block Diagram of a Half-Adder:-

Demonstrated a block diagram of a half-adder. Two half-adders can be combines to form an adder that can add three input digits. This is called a full-adder.