A combinational circuit is nothing but circuits that are created using simple gate. So logic is applied to the input and bits are sent directly to the output.

There is not MEMORY element like a flip-flop.

__HALF-ADDER CIRCUIT__

The simplest goal of this circuit is to add two bits and give the result. This circuit has 2 input and 2 output.

Outputs are

**SUM****CARRY**

Let us see what happens when you add two binary digits (OR)

1 + 0 = 1

0 + 1 = 1

0 + 0 = 0

1 + 1 = 0 and 1 as carry

**TRUTH TABLE OF HALF-ADDER**

**TRUTH TABLE OF HALF-ADDER**

TRUTH TABLE |

**C = x.y****S = x’.y + x.y’**

**The C carry is AND function.****The S sum is XOR function.**

**LOGIC DIAGRAM OF HALF-ADDER CIRCUIT**

**LOGIC DIAGRAM OF HALF-ADDER CIRCUIT**

From the Truth Table it is clear that we need two gate to implement the half-adder circuit.

HALF-ADDER CIRCUIT |

**FULL-ADDER CIRCUIT **

**FULL-ADDER CIRCUIT**

Full adder circuit needed when we want to add 3 bits which means there are 3 inputs to the circuit and 2 output.

The outputs are

**SUM****CARRY**

Let’s see what happens when we add three binary bits(OR).

**0 + 0 + 0 = 0**

**0 + 0 + 1 = 1**

**0 + 1 + 0 = 1**

**0 + 1 + 1 = 0 and carry = 1**

**1 + 0 + 0 = 1**

**1 + 0 + 1 = 0 and carry = 1**

**1 + 1 + 0 = 0 and carry = 1**

**1 + 1 + 1 = 1 and carry = 1**

It would be easier if we draw a Truth Table for the Full Adder circuit.

TRUTH TABLE FOR FULL-ADDER CIRCUIT |

#### **LOGIC DIAGRAM FOR FULL-ADDER CIRCUIT**

**LOGIC DIAGRAM FOR FULL-ADDER CIRCUIT**

We can find the characteristic equation of Full Adder circuit by using K-MAP. From the Truth table find all the minterms that give an sum = 1.

We get following,

Sum = x’y’z + x’yz’ + xy’z’ + xyz

The carry is 1 whenever two or more of three input variable is 1.

C = xy + xz + yz

FULL-ADDER K-MAP |

You can see that we cannot group any of these 1 in the K-MAP fro full adder. Hence,

Sum = m1 + m2 + m4 + m7

**FULL-ADDER LOGIC DIAGRAM**

**FULL-ADDER LOGIC DIAGRAM**

Construct full adder circuit diagram using two methods

- Construct using 2 Half-Adder circuits
- Implement using AND,OR and NOT gates.

CIRCUIT FOR CARRY |

CIRCUIT FOR SUM IN FULL-ADDER |

We will not see the circuit for Full Adder using two half-adder.

FULL ADDER CIRCUIT |