4 bit Adder Circuit

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.

1.      0011 + 0100 = 0111
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