• Theory:-

> A 4-bit Ripple Carry Adder (RCA) is a combinational circuit that adds two 4-bit binary numbers along with a carry input.

> Basic Unit:
  It is constructed by connecting four full adders in series each full adder adds corresponding bits of the two numbers along with the carry from the    previous stage.

> Working Principle:

• The sum and carry of each bit position are generated by the corresponding full adder.
  
  

• The carry-out of one full adder becomes the carry-in of the next adder this is called carry propagation.
  
  

> Carry Propagation Delay:
Since each adder must wait for the carry from its previous stage, the overall addition time increases linearly with the number of bits -  hence the name “ripple carry.”

   LOGIC DIAGRAM:

 TRUTH TABLE:

• Boolean Expression:-

> Bit 0:

sum 0 = a0 ⊕ b0 ⊕ c in

c1 = (a0 b0) + (b0 cin) + (cin a0)

> Bit 1: 

sum 1 = a1 ⊕ b1 ⊕ c1

c2 = (a1 b1) + (b1 c1) + (c1 a1)

> Bit 2: 

sum 2 = a2 ⊕ b2 ⊕ c2

c3 = (a2 b2) + (b2 c2) + (c2 a2)

> Bit 3: 

sum 3 = a3 ⊕ b3 ⊕ c3

cout = (a3 b3) + (b3 c3) + (c3 a3)