RCA

Theory

Definition:
The RCA is the simplest type of binary adder. It adds each bit sequentially, where the carry output from one full adder becomes the carry input for the next higher bit adder.

Working principle:
Each full adder waits for the carry from the previous stage before it can produce its own sum and carry.

Advantages:

• Simple design
  
  

• Easy to implement and understand
  
  

Disadvantages:

• Slow operation for large bit numbers because carry must “ripple” through each stage sequentially.
  
  

• Propagation delay increases linearly with the number of bits.

Truth Table

Boolean Expression

S = A​⊕B​⊕Cin

Cout = (A.B)+(B.Cin)+(A.Cin) 

Logic Circuit