Half Adder and Full Adder are the digital circuits that are used for simple addition. They have logic gates to perform binary digital additions.

**Half Adder:**

A half adder is a single bit adder. It has two inputs and two outputs. It consists of one EXOR logic gate producing **“SUM” **and one AND gate producing **“CARRY”**as outputs. It’s a 1-bit adder circuit that doesn’t have everything an adder circuit has.For instance, a half-adder may not have a carry input — useful for the least significant bit of a multi-bit adder. Or it may not have a carry output, useful for the most significant bit if you don’t want to handle overflow. With the help of half adder, we can design circuits that are capable of performing simple addition with the help of logic gates.

**INPUTS OUTPUTS**

**A B SUM CARRY**

0 0 0 0

0 1 1 0

1 0 1 0

1 1 0 1

**Full Adder:**

A full adder is a combinational circuit that forms the arithmetic sum of three input bits. It consists of three inputs and two outputs. Two of the input variables, denoted by x and y, represent the two significant bits to be added. The third input, z, represents the carry from the previous lower significant position. Two outputs are necessary because the arithmetic sum of three binary digits ranges in value from 0 to 3 and binary 2 or 3 needs two digits.

What makes it different from the half adder is that half adder does not take C (Carry-In) therefore full-adders can be cascaded for multibit summation.

### Applications Of Half Adder Full Adder-

There are many applications of Half Adder and Full Adder .These circuits are actually basic building of any digital electronics device . You can use these gates to make your own calculator.

you can use half adder and full adder to make other arithmetical and logical circuits like you can make your own **ALU **like this

The ALU (arithmetic logic circuitry) of a computer uses half adder to compute the binary addition operation on two bits.

Half adder is used to make full adder as a full adder requires 3 inputs, the third input being an input carry i.e. we will be able to cascade the carry bit from one adder to the other.

Ripple carry adder is possible to create a logical circuit using multiple full adders to add N-bit numbers. Each full adder inputs a C(in), which is the C(out) of the previous adder. This kind of adder is called RIPPLE CARRY ADDER, since each carry bit “ripples” to the next full adder. Note that the first full adder (and only the first) may be replaced by a half adder.