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
half-adder-using-xor-and.jpg half-adder-using-xor-and-inverters.jpg

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.


Block Diagram of a Half-Adder


Full-Adder Built From a Half-Adder:-

Demonstrated below the logic diagram of a full-adder, along with a block diagram that masks the details of the circuit.


Full-Adder Built From a Half-Adder:-
full-adder-built-from-half-adder.jpg full-adder-built-from-half-adder-block.jpg


Three Bit Adder Using Three Full-Adders:-


3 Bit Adder using three Full-adders


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