**Basic Theory:**

It
is possible to make a logical circuit using numerous full adders to add n-bit
numbers. In case of a four bit adder, the number of bits is four; hence it is a
4-bit adder. The main principle behind it is that, “

*each full adder inputs a Cin, which is the Cout of the previous adder*”. This kind of adder is called a ripple-carry adder or a parallel adder, since each carry bit "ripples" to the next full adder in parallel. We must note that the first (and only the first) full adder may be replaced by a half adder. The layout of a ripple-carry adder is simple, which allows for fast design time; however, the ripple-carry adder is relatively slow, since each full adder must wait for the carry bit to be calculated from the previous full adder.**Boolean Expressions (for Full Adder):**

S

_{n }= A**⊕**B**⊕**C
C

_{n}= BC + (B**⊕**C) A**Circuit Diagram:**

**Observed Values:**

Following set of values
were obtained in observation.

2. 1101 + 0001 = 1110

3. 1101 + 0010 = 1111

4. 0010 + 0010 = 0100

5. 1000 + 1000 = 0000; Cout = 1

**Reference:**

Wikipedia (2013), Adder
(electronics),

*Ripple-carry Adder*, Accessed: February 8, 2013, Retrieved from: http://en.wikipedia.org/wiki/Adder_%28electronics%29#Ripple-carry_adder
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