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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 |
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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 |
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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:- | |
|---|---|
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Three Bit Adder Using Three Full-Adders:-
| 3 Bit Adder using three Full-adders |
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