CLA

Theory

Definition:
The CLA is a faster adder circuit that reduces carry propagation delay by generating carry signals in advance using generate (G) and propagate (P) functions.

Working principle:

• Generate (Gᵢ) = Aᵢ · Bᵢ — a carry is generated at bit i.
  
  

• Propagate (Pᵢ) = Aᵢ ⊕ Bᵢ — a carry is propagated through bit i.
  
  

• Carries are computed directly using Boolean equations instead of waiting sequentially.
  
  

Advantages:

• Much faster than RCA since carry bits are computed in parallel.
  
  

Disadvantages:

• More complex hardware and wiring.
  
  

• Not practical for very high bit adders unless combined hierarchically (e.g., in Carry Look-Ahead Blocks).

Truth Table

Boolean Expression

Expressions :

• Pi = Ai ^ Bi    

• Gi = Ai & Bi   

Carry equations:  

• Ci=Gi-1|(pi-1&Ci-1)

• C0 = cin

• C1 = G0 | (P0 & C0)

• C2 = G1 | (P1 & C1) = G1 | (P1 & G0) | (P1 & P0 & C0)

• C3 = G2 | (P2 & C2) = G2 | (P2 & G1) | (P2 & P1 & G0) | (P2 & P1 & P0 & C0)

• C4 = G3 | (P3 & C3) = G3 | (P3 & G2) | (P3 & P2 & G1) | (P3 & P2 & P1 & G0) | (P3 & P2 & P1 & P0 & C0)

Sum

• Si = Pi ^ Ci

Logic Circuit