# Full Adder : It’s Truth table, Circuit Diagram

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Full adder is a combinational logic circuit perform addition of three single bit number. It is a digital circuit has three inputs A, B and Cin , where Cin is the previous carry and two output sum (S), carry (Cout). Here sum is the least significant bit (LSB) and carry is the most significant bit (MSB). Full adder circuit is used in computer ALU (Arithmetic and Logic Unit ) to perform arithmetic operation.

## Truth Table of Full Adder

The full adder circuit perform OR (addition) operation between two single bit binary number A,B and previous carry Cin. Basically, a full adder is a three input and two output combinational circuit. Three inputs A,B and Cin having eight input combinations. After addition of three single bit binary number this circuit produces two outputs Sum (S) and carry (Cout).

Truth table explain the relationship between inputs and outputs.

In the above table,

1. A and B are the two single bit inputs and Cin is the previous carry. So, three inputs having 23 = 8 Possible combination.
2. When we perform OR operation between three inputs, it produces two output sum (s) and carry (c).
3. Here sum is the least significant bit (LSB) and carry is the most significant bit (MSB).
4. Carry output is “1” only when the sum of inputs are greater then “1”.
5. The least significant bit of the addition is defined by the ‘sum’ bit.

Now, To find the Boolean logical expression from truth table make a k-map for outputs Sum (S) and carry (Cout) and get Boolean expression in SOP form.

## K-Map for the Sum Output

Expression for sum after solving k-map

Sum =A xor B xor Cin

## K-Map for Cout

Expression for Cout after solving k-map

Co = AB + ACin +BCin

Now draw the logic diagram of Full adder

## A Logic Diagram For Full Adder

For more detail watch my video

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